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<h2>HL Paper 2</h2><div class="specification">
<p>A planet has radius <em>R</em>. At a distance <em>h </em>above the surface of the planet the gravitational field strength is <em>g </em>and the gravitational potential is <em>V</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by gravitational field strength.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <em>V </em>= –<em>g</em>(<em>R </em>+ <em>h</em>).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a graph, on the axes, to show the variation of the gravitational potential <em>V</em> of the planet with height <em>h </em>above the surface of the planet.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A planet has a radius of 3.1 × 10<sup>6</sup> m. At a point P a distance 2.4 × 10<sup>7</sup> m above the surface of the planet the gravitational field strength is 2.2 N kg<sup>–1</sup>. Calculate the gravitational potential at point P, include an appropriate unit for your answer.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The diagram shows the path of an asteroid as it moves past the planet.</p>
<p> <img src="images/Schermafbeelding_2018-08-14_om_07.33.17.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/06.c"></p>
<p>When the asteroid was far away from the planet it had negligible speed. Estimate the speed of the asteroid at point P as defined in (b).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The mass of the asteroid is 6.2 × 10<sup>12</sup> kg. Calculate the gravitational force experienced by the <strong>planet </strong>when the asteroid is at point P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the <strong>«</strong>gravitational<strong>» </strong>force per unit mass exerted on a point/small/test mass</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>at height <em>h </em>potential is <em>V</em> = –<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{GM}}{{(R + h)}}">
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mi>R</mi>
<mo>+</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
</mrow>
</mfrac>
</math></span></p>
<p>field is <em>g </em>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{GM}}{{{{(R + h)}^2}}}">
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mi>R</mi>
<mo>+</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p><strong>«</strong>dividing gives answer<strong>»</strong></p>
<p> </p>
<p><em>Do not allow an answer that starts with g = –</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\Delta V}}{{\Delta r}}">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>V</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>r</mi>
</mrow>
</mfrac>
</math></span><em> and then cancels the deltas and substitutes </em><em>R </em>+ <em>h</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct shape and sign</p>
<p>non-zero negative vertical intercept</p>
<p> </p>
<p><img src="images/Schermafbeelding_2018-08-14_om_07.26.11.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/06.a.iii/M"></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>V</em> = <strong>«</strong>–2.2 × (3.1 × 10<sup>6</sup> + 2.4 × 10<sup>7</sup>) =<strong>»</strong> <strong>«</strong>–<strong>»</strong> 6.0 × 10<sup>7</sup> J kg<sup>–1</sup></p>
<p> </p>
<p><em>Unit is essential</em></p>
<p><em>Allow eg MJ kg<sup>–</sup></em><em><sup>1</sup> </em><em>if power of 10 is correct</em></p>
<p><em>Allow other correct SI units eg m</em><sup><em>2</em></sup><em>s<sup>–</sup></em><sup><em>2</em></sup><em>, N m kg<sup>–</sup></em><sup><em>1</em></sup></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total energy at P = 0 / KE gained = GPE lost</p>
<p><strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>mv</em><sup>2</sup> + <em>mV</em> = 0 ⇒<strong>»</strong> <em>v</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt { - 2V} ">
<msqrt>
<mo>−</mo>
<mn>2</mn>
<mi>V</mi>
</msqrt>
</math></span></p>
<p><em>v</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2 \times 6.0 \times {{10}^7}} ">
<msqrt>
<mn>2</mn>
<mo>×</mo>
<mn>6.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>7</mn>
</msup>
</mrow>
</msqrt>
</math></span> =<strong>»</strong> 1.1 × 10<sup>4</sup> <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p> </p>
<p><em>Award </em><strong><em>[3] </em></strong><em>for a bald correct answer</em></p>
<p><em>Ignore negative sign errors in the workings</em></p>
<p><em>Allow ECF from 6(b)</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p>force on asteroid is <strong>«</strong>6.2 × 10<sup>12</sup> × 2.2 =<strong>»</strong> 1.4 × 10<sup>13</sup> <strong>«</strong>N<strong>»</strong></p>
<p><strong>«</strong>by Newton’s third law<strong>» </strong>this is also the force on the planet</p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>mass of planet = 2.4 x 10<sup>25</sup> <strong>«</strong>kg<strong>» «</strong>from <em>V</em> = –<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{GM}}{{(R + h)}}">
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mi>R</mi>
<mo>+</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
</mrow>
</mfrac>
</math></span><strong>»</strong></p>
<p>force on planet <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{GMm}}{{{{(R + h)}^2}}}">
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
<mi>m</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mi>R</mi>
<mo>+</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span><strong>»</strong> = 1.4 × 10<sup>13</sup> <strong>«</strong>N<strong>»</strong></p>
<p> </p>
<p><em>MP2 must be explicit</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Hydrogen atoms in an ultraviolet (UV) lamp make transitions from the first excited state to the ground state. Photons are emitted and are incident on a photoelectric surface as shown.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-13_om_12.49.40.png" alt="M18/4/PHYSI/HP2/ENG/TZ1/08"></p>
</div>
<div class="specification">
<p>The photons cause the emission of electrons from the photoelectric surface. The work function of the photoelectric surface is 5.1 eV.</p>
</div>
<div class="specification">
<p>The electric potential of the photoelectric surface is 0 V. The variable voltage is adjusted so that the collecting plate is at –1.2 V.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the energy of photons from the UV lamp is about 10 eV.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in J, the maximum kinetic energy of the emitted electrons.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest, with reference to conservation of energy, how the variable voltage source can be used to stop all emitted electrons from reaching the collecting plate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The variable voltage can be adjusted so that no electrons reach the collecting plate. Write down the minimum value of the voltage for which no electrons reach the collecting plate.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>E</em><sub>1</sub> = –13.6 <strong>«</strong>eV<strong>»</strong> E<sub>2</sub> = – <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{13.6}}{4}">
<mfrac>
<mrow>
<mn>13.6</mn>
</mrow>
<mn>4</mn>
</mfrac>
</math></span> = –3.4 <strong>«</strong>eV<strong>»</strong></p>
<p>energy of photon is difference <em>E</em><sub>2</sub> – <em>E</em><sub>1</sub> = 10.2 <strong>«</strong>≈ 10 eV<strong>»</strong></p>
<p> </p>
<p><em>Must see at least 10.2 eV.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>10 – 5.1 = 4.9 <strong>«</strong>eV<strong>»</strong></p>
<p>4.9 × 1.6 × 10<sup>–19</sup> = 7.8 × 10<sup>–19</sup> <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Allow </em>5.1 <em>if </em>10.2 <em>is used to give</em> 8.2×10<sup>−19</sup> <strong>«</strong>J<strong>»</strong>.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>EPE produced by battery</p>
<p>exceeds maximum KE of electrons / electrons don’t have enough KE</p>
<p> </p>
<p><em>For first mark, accept explanation in terms of electric potential energy difference of electrons between surface and plate.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>4.9 <strong>«</strong>V<strong>»</strong></p>
<p> </p>
<p><em>Allow 5.1 if 10.2 is used in (b)(i).</em></p>
<p><em>Ignore sign on answer.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>two equally spaced vertical lines (judge by eye) at approximately 1/3 and 2/3</p>
<p>labelled correctly</p>
<p><img src="images/Schermafbeelding_2018-08-13_om_14.47.13.png" alt="M18/4/PHYSI/HP2/ENG/TZ1/08.c.i/M"></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>kinetic energy at collecting plate = 0.9 <strong>«</strong>eV<strong>»</strong></p>
<p>speed = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{2 \times 0.9 \times 1.6 \times {{10}^{ - 19}}}}{{9.11 \times {{10}^{ - 31}}}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>0.9</mn>
<mo>×</mo>
<mn>1.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>19</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>9.11</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>31</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span><strong>»</strong> = 5.6 × 10<sup>5</sup> <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Allow ECF from MP1</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A metal sphere is charged positively and placed far away from other charged objects. The electric potential at a point on the surface of the sphere is 53.9 kV.</p>
</div>
<div class="specification">
<p>A small positively charged object moves towards the centre of the metal sphere. When the object is 2.8 m from the centre of the sphere, its speed is 3.1 m s<sup>−1</sup>. The mass of the object is 0.14 g and its charge is 2.4 × 10<sup>−8 </sup>C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by electric potential at a point.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The electric potential at a point a distance 2.8 m from the centre of the sphere is 7.71 kV. Determine the radius of the sphere.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Comment on the angle at which the object meets equipotential surfaces around the sphere.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the kinetic energy of the object is about 0.7 mJ.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine whether the object will reach the surface of the sphere.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the work done per unit charge ✓</p>
<p>In bringing a small/point/positive/test «charge» from infinity to the point ✓</p>
<p> </p>
<p><em>Allow use of energy per unit charge for <strong>MP1</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of<em> Vr</em> = constant ✓</p>
<p>0.40 m ✓</p>
<p> </p>
<p><em>Allow <strong>[1]</strong> max if r + 2.8 used to get 0.47 m.</em></p>
<p><em>Allow <strong>[2]</strong> marks if they calculate Q at one potential and use it to get the distance at the other potential.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>90° / perpendicular ✓</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>0</mn><mo>.</mo><mn>14</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>.</mo><msup><mn>1</mn><mn>2</mn></msup></math> <em><strong>OR </strong> </em>0.67 «mJ» seen ✓</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«p.d. between point and sphere surface = » (53.9 kV – 7.71) «kV» <em><strong>OR </strong></em>46.2 «kV» seen ✓</p>
<p>«energy required =» VQ « = 46 200 × 2.4 × 10<sup>-8</sup>» = 1.11 mJ ✓</p>
<p>this is greater than kinetic energy so will not reach sphere ✓</p>
<p> </p>
<p><em><strong>MP3</strong> is for a conclusion consistent with the calculations shown.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>a) Well answered.</p>
<p>b) Generally, well answered, but there were quite a few using r + 2.8.</p>
<p>ci) Very few had problems to recognize the perpendicular angle</p>
<p>cii) Good simple calculation</p>
<p>ciii) Many had a good go at this, but a significant number tried to answer it based on forces.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what is meant by the gravitational potential at the surface of a planet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An unpowered projectile is fired vertically upwards into deep space from the surface of planet Venus. Assume that the gravitational effects of the Sun and the other planets are negligible.</p>
<p>The following data are available.</p>
Mass of Venus
= 4.87×10<sup>24</sup> kg
Radius of Venus
= 6.05×10<sup>6</sup> m
Mass of projectile
= 3.50×10<sup>3</sup> kg
Initial speed of projectile
= 1.10×escape speed
<p> </p>
<p>(i) Determine the initial kinetic energy of the projectile.</p>
<p>(ii) Describe the subsequent motion of the projectile until it is effectively beyond the gravitational field of Venus.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the «gravitational» work done «by an external agent» per/on unit mass/kg</p>
<p><em>Allow definition in terms of reverse process of moving mass to infinity eg “work done on external agent by…”.<br>Allow “energy” as equivalent to “work done”</em></p>
<p>in moving a «small» mass from infinity to the «surface of» planet / to a point</p>
<p><em><strong>N.B</strong>.: on SL paper Q5(a)(i) and (ii) is about “gravitational field”.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i<br>escape speed<br><em>Care with ECF from MP1.</em></p>
<p><em>v</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\left( {\frac{{2\,{\text{GM}}}}{R}} \right)} = ">
<msqrt>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>2</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>GM</mtext>
</mrow>
</mrow>
<mi>R</mi>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</msqrt>
<mo>=</mo>
</math></span>»</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\left( {\frac{{2 \times 6.67 \times {{10}^{ - 11}} \times 4.87 \times {{10}^{24}}}}{{6.05 \times {{10}^6}}}} \right)} ">
<msqrt>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>6.67</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>11</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>4.87</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>24</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>6.05</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>6</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</msqrt>
</math></span> <em><strong>or</strong></em> 1.04×10<sup>4</sup>«<em>m s<sup>–</sup></em><sup>1</sup>»<br><br><em><strong>or</strong></em> «1.1 × 1.04 × 10<sup>4 </sup>m s<sup>-1</sup>»= 1.14 × 10<sup>4 </sup>«m s<em><sup>–</sup></em><sup>1</sup>»</p>
<p>KE = «0.5 × 3500 × (1.1 × 1.04 × 10<sup>4 </sup>m s<em><sup>–</sup></em><sup>1</sup>)<sup>2 </sup>=» 2.27×10<sup>11 </sup>«J»</p>
<p><em>Award <strong>[1 max]</strong> for omission of 1.1 – leads to 1.88×10<sup>11 </sup>m s<sup>-1</sup>.</em><br><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<p> </p>
<p>ii<br>Velocity/speed decreases / projectile slows down «at decreasing rate»</p>
<p>«magnitude of» deceleration decreases «at decreasing rate»<br><em>Mention of deceleration scores MP1 automatically.</em></p>
<p>velocity becomes constant/non-zero <br><em><strong>OR</strong></em><br>deceleration tends to zero</p>
<p><em>Accept “negative acceleration” for “deceleration”.</em></p>
<p><em>Must see “velocity” not “speed” for MP3.</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The gravitational potential due to the Sun at its surface is –1.9 x 10<sup>11</sup> J kg<sup>–1</sup>. The following data are available.</p>
<table style="width: 441.4px; margin-left: 120px;">
<tbody>
<tr>
<td style="width: 422px;">Mass of Earth</td>
<td style="width: 558.4px;">= 6.0 x 10<sup>24</sup> kg</td>
</tr>
<tr>
<td style="width: 422px;">Distance from Earth to Sun</td>
<td style="width: 558.4px;">= 1.5 x 10<sup>11</sup> m</td>
</tr>
<tr>
<td style="width: 422px;">Radius of Sun</td>
<td style="width: 558.4px;">= 7.0 x 10<sup>8</sup> m</td>
</tr>
</tbody>
</table>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the gravitational potential is negative.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The gravitational potential due to the Sun at a distance <em>r</em> from its centre is <em>V</em><sub>S</sub>. Show that</p>
<p><em>rV</em><sub>S</sub> = constant.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the gravitational potential energy of the Earth in its orbit around the Sun. Give your answer to an appropriate number of significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the total energy of the Earth in its orbit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An asteroid strikes the Earth and causes the orbital speed of the Earth to suddenly decrease. Suggest the ways in which the orbit of the Earth will change.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, in terms of the force acting on it, why the Earth remains in a circular orbit around the Sun.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>potential is defined to be zero at infinity</p>
<p>so a positive amount of work needs to be supplied for a mass to reach infinity</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>V</em><sub>S</sub> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{{GM}}{r}">
<mo>−</mo>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> so <em>r</em> x <em>V</em><sub>S</sub> «= –<em>GM</em>» = constant because<em> G</em> and<em> M</em> are constants</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>GM</em> = 1.33 x 10<sup>20</sup> «J m kg<sup>–1</sup>»</p>
<p>GPE at Earth orbit «= –<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.33 \times {{10}^{20}} \times 6.0 \times {{10}^{24}}}}{{1.5 \times {{10}^{11}}}}">
<mfrac>
<mrow>
<mn>1.33</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>20</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>6.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>24</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>11</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>» = «–» 5.3 x 10<sup>33</sup> «J»</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> unless answer is to 2 sf.</em></p>
<p><em>Ignore addition of Sun radius to radius of Earth orbit.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>work leading to statement that kinetic energy <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{GMm}}{{2r}}">
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
<mi>m</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>r</mi>
</mrow>
</mfrac>
</math></span>, <em><strong>AND</strong></em> kinetic energy evaluated to be «+» 2.7 x 10<sup>33</sup> «J»</p>
<p>energy «= PE + KE = answer to (b)(ii) + 2.7 x 10<sup>33</sup>» = «–» 2.7 x 10<sup>33</sup> «J»</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>statement that kinetic energy is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = - \frac{1}{2}">
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> gravitational potential energy in orbit</p>
<p>so energy «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{{\text{answer to (b)(ii)}}}}{2}">
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mtext>answer to (b)(ii)</mtext>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
</math></span>» = «–» 2.7 x 10<sup>33</sup> «J»</p>
<p> </p>
<p><em>Various approaches possible.</em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«KE will initially decrease so» total energy decreases<br><em><strong>OR</strong></em><br>«KE will initially decrease so» total energy becomes more negative</p>
<p>Earth moves closer to Sun</p>
<p>new orbit with greater speed «but lower total energy»</p>
<p>changes ellipticity of orbit</p>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>centripetal force is required</p>
<p>and is provided by gravitational force between Earth and Sun</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> for statement that there is a “centripetal force of gravity” without further qualification.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>There is a proposal to power a space satellite X as it orbits the Earth. In this model, X is connected by an electronically-conducting cable to another smaller satellite Y.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Satellite Y orbits closer to the centre of Earth than satellite X. Outline why</p>
</div>
<div class="specification">
<p>The cable acts as a spring. Satellite Y has a mass <em>m</em> of 3.5 x 10<sup>2</sup> kg. Under certain circumstances, satellite Y will perform simple harmonic motion (SHM) with a period <em>T</em> of 5.2 s.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Satellite X orbits 6600 km from the centre of the Earth.</p>
<p>Mass of the Earth = 6.0 x 10<sup>24</sup> kg</p>
<p>Show that the orbital speed of satellite X is about 8 km s<sup>–1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the orbital times for X and Y are different.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>satellite Y requires a propulsion system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The cable between the satellites cuts the magnetic field lines of the Earth at right angles.</p>
<p><img 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"></p>
<p>Explain why satellite X becomes positively charged.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Satellite X must release ions into the space between the satellites. Explain why the current in the cable will become zero unless there is a method for transferring charge from X to Y.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The magnetic field strength of the Earth is 31 μT at the orbital radius of the satellites. The cable is 15 km in length. Calculate the emf induced in the cable.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the value of <em>k</em> in the following expression.</p>
<p><em>T</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi \sqrt {\frac{m}{k}} ">
<mn>2</mn>
<mi>π</mi>
<msqrt>
<mfrac>
<mi>m</mi>
<mi>k</mi>
</mfrac>
</msqrt>
</math></span></p>
<p>Give an appropriate unit for your answer. Ignore the mass of the cable and any oscillation of satellite X.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the energy changes in the satellite Y-cable system during one cycle of the oscillation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \sqrt {\frac{{G{M_E}}}{r}} ">
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>G</mi>
<mrow>
<msub>
<mi>M</mi>
<mi>E</mi>
</msub>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</msqrt>
</math></span>» = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{6.67 \times {{10}^{ - 11}} \times 6.0 \times {{10}^{24}}}}{{6600 \times {{10}^3}}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>6.67</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>11</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>6.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>24</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>6600</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span></p>
<p>7800 «m s<sup>–1</sup>»</p>
<p><em>Full substitution required</em></p>
<p><em>Must see 2+ significant figures.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Y has smaller orbit/orbital speed is greater so time period is less</p>
<p><em>Allow answer from appropriate equation</em></p>
<p><em>Allow converse argument for X</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>to stop Y from getting ahead</p>
<p>to remain stationary with respect to X</p>
<p>otherwise will add tension to cable/damage satellite/pull X out of its orbit</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>cable is a conductor and contains electrons</p>
<p>electrons/charges experience a force when moving in a magnetic field</p>
<p>use of a suitable hand rule to show that satellite Y becomes negative «so X becomes positive»</p>
<p><em><strong>Alternative 2</strong></em></p>
<p>cable is a conductor</p>
<p>so current will flow by induction flow when it moves through a B field</p>
<p>use of a suitable hand rule to show current to right so «X becomes positive»</p>
<p><em>Marks should be awarded from either one alternative or the other.</em></p>
<p><em>Do not allow discussion of positive charges moving towards X</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>electrons would build up at satellite Y/positive charge at X</p>
<p>preventing further charge flow</p>
<p>by electrostatic repulsion</p>
<p>unless a complete circuit exists</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<em>ε</em> = <em>Blv =</em>» 31 x 10<sup>–6</sup> x 7990 x 15000</p>
<p>3600 «V»</p>
<p><em>Allow 3700 «V» from v = 8000 m s<sup>–1</sup>.</em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <em>k</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4{\pi ^2}m}}{{{T^2}}} = ">
<mfrac>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>m</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4 \times {\pi ^2} \times 350}}{{{{5.2}^2}}}">
<mfrac>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>350</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mn>5.2</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>510</p>
<p>N m<sup>–1</sup> <em><strong>or</strong> </em>kg s<sup>–2</sup></p>
<p><em>Allow MP1 and MP2 for a bald correct answer</em></p>
<p><em>Allow 500</em></p>
<p><em>Allow N/m etc.</em></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>E</em><sub>p</sub> in the cable/system transfers to <em>E</em><sub>k</sub> of Y</p>
<p>and back again twice in each cycle</p>
<p><em>Exclusive use of gravitational potential energy negates MP1</em></p>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The table gives data for Jupiter and three of its moons, including the radius <em>r</em> of each object.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A spacecraft is to be sent from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Io</mtext></math> to infinity.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, for the surface of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Io</mtext></math>, the gravitational field strength <em>g</em><sub>Io</sub> due to the mass of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Io</mtext></math>. State an appropriate unit for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>gravitational</mi><mo> </mo><mi>potential</mi><mo> </mo><mi>due</mi><mo> </mo><mi>to</mi><mo> </mo><mi>Jupiter</mi><mo> </mo><mi>at</mi><mo> </mo><mi>the</mi><mo> </mo><mi>orbit</mi><mo> </mo><mi>of</mi><mo> </mo><mi>Io</mi></mrow><mrow><mo> </mo><mi>gravitational</mi><mo> </mo><mi>potential</mi><mo> </mo><mi>due</mi><mo> </mo><mi>to</mi><mo> </mo><mi>Io</mi><mo> </mo><mi>at</mi><mo> </mo><mi>the</mi><mo> </mo><mi>surface</mi><mo> </mo><mi>of</mi><mo> </mo><mi>Io</mi></mrow></mfrac></math> is about 80.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, using (b)(i), why it is not correct to use the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>2</mn><mi>G</mi><mo>×</mo><mtext>mass of Io</mtext></mrow><mtext>radius of Io</mtext></mfrac></msqrt></math> to calculate the speed required for the spacecraft to reach infinity from the surface of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Io</mtext></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation. </p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mfrac><mrow><mi>G</mi><mi>M</mi></mrow><msup><mi>r</mi><mn>2</mn></msup></mfrac><mo>=</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>×</mo><mn>8</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></mrow><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>»</mo><mn>1</mn><mo>.</mo><mn>8</mn></math><strong> ✓</strong></p>
<p>N kg<sup>−1 </sup><em><strong>OR</strong> </em>m s<sup>−2</sup><strong> ✓</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>27</mn></msup></mrow><mrow><mn>4</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow></mfrac></math><strong> <em>AND </em> </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac></math><strong> </strong>seen<strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>27</mn></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow><mrow><mn>4</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup><mo>×</mo><mn>8</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></mrow></mfrac><mo>=</mo><mo>»</mo><mn>78</mn></math><strong> ✓</strong></p>
<p><em><br>For <strong>MP1</strong>, potentials can be seen individually or as a ratio.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«this is the escape speed for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Io</mtext></math> alone but» gravitational potential / field of Jupiter must be taken into account<strong> ✓</strong></p>
<p><em><strong><br>OWTTE</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>G</mi><msub><mi>M</mi><mtext>Jupiter</mtext></msub><mfenced><mrow><mfrac><mn>1</mn><mrow><mn>1</mn><mo>.</mo><mn>88</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>.</mo><mn>06</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfrac></mrow></mfenced><mo>=</mo><mo>«</mo><mn>5</mn><mo>.</mo><mn>21</mn><mo>×</mo><msup><mn>10</mn><mn>7</mn></msup><mo> </mo><msup><mtext>J kg</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math><strong> ✓</strong></p>
<p>« multiplies by 3600 kg to get » 1.9 × 10<sup>11 </sup>«J» <strong>✓</strong></p>
<p><em><br>Award <strong>[2]</strong> marks if factor of ½ used, taking into account orbital kinetic energies, leading to a final answer of 9.4 x 10<sup>10 </sup>«J».</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong></em></p>
<p><em>Award <strong>[2] marks</strong> for a bald correct answer.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the electric field lines of a positively charged conducting sphere of radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> and charge <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" width="352" height="213"></p>
<p>Points A and B are located on the same field line.</p>
</div>
<div class="specification">
<p>A proton is placed at A and released from rest. The magnitude of the work done by the electric field in moving the proton from A to B is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>16</mn></mrow></msup><mo> </mo><mi mathvariant="normal">J</mi></math>. Point A is at a distance of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math> from the centre of the sphere. Point B is at a distance of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math> from the centre of the sphere.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the electric potential decreases from A to B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, on the axes, the variation of electric potential <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> with distance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> from the centre of the sphere.</p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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" width="336" height="236"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the electric potential difference between points A and B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the charge <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math> of the sphere.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The concept of potential is also used in the context of gravitational fields. Suggest why scientists developed a common terminology to describe different types of fields.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><em><strong>ALTERNATIVE 1</strong></em><br></span><span class="fontstyle2">work done on moving a positive test charge in any outward direction is negative </span><span class="fontstyle3">✓<br></span><span class="fontstyle2">potential difference is proportional to this work </span><span class="fontstyle4">«</span><span class="fontstyle2">so </span><span class="fontstyle5"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> </span><span class="fontstyle2">decreases from A to B</span><span class="fontstyle4">» </span><span class="fontstyle3">✓</span></p>
<p> </p>
<p><span class="fontstyle0"><em><strong>ALTERNATIVE 2</strong></em><br></span><span class="fontstyle2">potential gradient is directed opposite to the field so inwards </span><span class="fontstyle3">✓<br></span><span class="fontstyle2">the gradient indicates the direction of increase of </span><span class="fontstyle4"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> </span><span class="fontstyle5">«</span><span class="fontstyle2">hence </span><span class="fontstyle4"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> </span><span class="fontstyle2">increases towards the centre/decreases from A to B</span><span class="fontstyle5">» </span><span class="fontstyle3">✓</span></p>
<p> </p>
<p><span class="fontstyle0"><em><strong>ALTERNATIVE 3</strong></em><br></span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mi>k</mi><mi>Q</mi></mrow><mi>R</mi></mfrac></math> </span><span class="fontstyle3">so as </span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> </span><span class="fontstyle3">increases </span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> </span><span class="fontstyle3">decreases </span><span class="fontstyle4">✓<br></span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> </span><span class="fontstyle3">is positive as </span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math> </span><span class="fontstyle3">is positive </span><span class="fontstyle4">✓</span></p>
<p><span class="fontstyle2"> </span></p>
<p><span class="fontstyle0"><em><strong>ALTERNATIVE 4</strong></em><br></span><span class="fontstyle2">the work done per unit charge in bringing a positive charge from infinity </span><span class="fontstyle3">✓<br></span><span class="fontstyle2">to point B is less than point A </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">curve decreasing asymptotically for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>></mo><mi>R</mi></math> </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">non <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math> zero constant between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and </span><span class="fontstyle3"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> </span><span class="fontstyle2">✓</span></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASsAAADWCAYAAACJ36THAAAXiUlEQVR4Ae2dV6xVxduHufHKC70wotEgMSqIvUSNN8RoMIgNFVDshSIgIkVQmkrvWAALYBRFUaQoIEqxYKOIioKABRURRFCailjef37zZfGts88cOLtx9ux5JtnZa89aa++Z513nd6a8804tI0EAAhAIgECtAMpIESEAAQgYYsVDAAEIBEEAsQrCTBQSAhDIS6x27dplkyZNsm3btkESAhCAQFEJ5CxWO3bssB49eliTJk2se/futmXLlqIWlC+HAATiJpCTWEmYevbsaStWrLA+ffrYwoUL7cEHH0Sw4n6WqD0Eikoga7HavXu3jRkzxpYtW+YK1rdvX9u5c6f73L9//6IWli+HAATiJZC1WAmVxqqSlIhVZn5ynncIQAAChSCQk1ilfzgtVul8jiEAAQgUkkDBxOqff/6xLl26uLGr//77r1IZx40bZ61atbI9e/ZUOkcGBCAAgf0RKJhY6Yfmz59vRx55pG3fvr3C70q8GjRoYBMmTKiQzwcIQAAC1SVQULHSWFb9+vVt6tSpFX5/6dKlduihh9rmzZsr5PMBAhCAQHUJFFSs1ILSGFazZs1Ms4ZK//77r3Xo0MHatGlj6iqSIAABCORCoKBipQKsX7/eateubWvWrHHl2bRpkx1++OG2ePHiXMrHPRCAAAQcgYKLlb714osvtn79+rkfmDhxoh177LHghgAEIJAXgaKI1eTJk61hw4a2YcMGtxxnxIgReRWSmyEAAQgURaw0G1ivXj0bOXKk1alTx9atWwdpCEAAAnkRKIpYqUSdO3e2unXrWtOmTfMqIDdDAAIQEIGiiZXcFRo1amRz586FNAQgAIG8CRRNrPIuGV8AAQhAIEUAsUrB4BACEChdAohV6dqGkkEAAikCiFUKBocQgEDpEkCsStc2lAwCEEgRQKxSMDiEAARKlwBiVbq2oWQQgECKAGKVgsEhBCBQugQQq9K1DSWDAARSBBCrFAwOIQCB0iWAWJWubSgZBCCQIoBYpWBwCAEIlC4BxKp0bUPJIACBFAHEKgWDQwhAoHQJIFalaxtKBgEIpAggVikYHEIAAqVLIG+x6tOnj9vUVNtwpV/agiv5XNVx5vn0dTqX/lzVceZ3JPcl1yfvSX7m9b7zytOLBAEIlA6BvMRq48aN1rhxYxs4cKCNHj3atDFE8ho6dKj3eNiwYS5/+PDhe88nebpH+ckrydd3DhkypML1yf3Je/ra5Ht0X5Kv63xlSuclv6H3Tp062erVq0vHUpQEApETyFusLrjgAuvYsaP1799/72vw4MF7j9P5Oh4wYIATt8x8bd119913u/sy78/8nHnvoEGDKvxe165d7aGHHrLM/OQ+iWuPHj2sV69eFe6TQKkcele92rZta7/99lvkjwjVh0BpEMhLrFSF3r1726+//up2W9aOy+nX33//7T5nvifXJPn6rOM9e/Z478+8Prkvec88r+9Jn0uOk3ddn1zjy9u5c6eNHz/errjiCidou3btKg1rUQoIREwgb7HSdvH64y6npPo0a9bMxo4dazfddJONGjXKiVs51ZG6QCA0AoiVx2Lq+kms3nvvPVuwYIG1bNnStHGrWmEkCECgZgggVh7u27ZtsxtuuMEWL17sBGr69Ol29dVX28yZM1031XMLWRCAQJEJIFYewBrTWrFixd7urT5PnDjRrrnmGnvzzTcRLA8zsiBQbAKIVRaENeh+7bXX2pw5cxCsLLhxKQQKQQCx8lD8/fffnX/WqlWrKpzVmNVTTz3lxrBmzJiBYFWgwwcIFJcAYuXhmx5gzzz9119/uS7h9ddfb9OmTUOwMgHxGQJFIoBYecBKrJo3b+5mAz2nbffu3fbMM8+4GcMXX3zRffZdRx4EIFA4AoiVh+X27dutdevWbjbQc9plqUuYzBLKH0v3kCAAgeIRQKzyZLto0SLn1nD//ffbli1b8vw2bocABKoigFhVRSaL/JUrV9ott9ziWmNff/11FndyKQQgUF0CiJWHlLp0t9122z67gZm3ff/9924doVwb5s+fT4iZTEB8hkCeBBArD0ANsLdo0cLUxcsmaUH3uHHj7KqrrnIuDjt27Mjmdq6FAAT2QQCx8sCRWElw3n//fc/ZfWcpmoNcGrQAWiFo1q5d64IQ7vsuzkIAAvsjgFh5CMmXat68efbLL794zlYvS4H77rrrLrv55pvt9ddfZxF09bBxFQSqJIBYVYkm/xMKNTNhwgRr2rSpPfDAAwTyyx8p3xAxAcTKY3w5fc6aNcs2bNjgOZtdlmK+L1u2zNq3b+/WFc6ePZvYWNkh5GoIOAKIledBSMasPvzwQ8/Z3LI02P7YY4/ZddddZz179jS5O7ApRW4suStOAoiVx+5yXVA4GAXfK2RSqJmlS5e6+O8agNei6E2bNhXyJ/guCJQtAcTKY1qJlfylPvjgA8/Z/LMU011LdSRYWtYjvyyNb6nLSIIABPwEECsPF80GfvTRR7Z161bP2cJl/fDDDzZy5EjnJtG9e3c3tkXo5MLx5ZvKiwBiVQL2XLNmjdslSLvpdOvWzZYvX14CpaIIECgtAoiVxx5qWT3xxBN2INf5qUX18ccfOxcHida9997rlvvIyZQEAQiYIVaep0CzgRpgz8WD3fN1WWX98ccfrmXVp08fF5FUovXOO+/sjQef1ZdxMQTKiABi5TFmIlaFdF3w/Mw+syRaamlpZ2nttKPdqrVZxebNmxmI3yc5TpYrAcTKY1nNBt55551OLDynD2iWuoGfffaZDR8+3C2ubteunYtS+u233+JcekAtwY/VNAHEqqYtkMXvf/fdd/b000+7lpacS/v37+9mELXBBW4PWYDk0iAJIFYBmk1dxLlz5zpP+EsvvdTatm1rzz77rH311VdsYBGgPSly9QggVh5O2pFZ0RKK5RTq+cmcsjRrqdaWlvGoe6hdo7t27Wqvvfaabdy4kdZWTlS5qVQJIFYey2iAXX/4NTnA7ilWlVlaY6jAf1oeNHDgQLv11ltNW4Xp+N1337WffvqJdYhV0uNEKAQQK4+lQhOrdBXkr7V+/Xo3c6hNLBSeuVWrVtavXz97++23XSQJfLfSxDgOhQBi5bGUBqxnzpxpiqseclKLS0t6Xn31Vdc91HpHrUeUcCmaqbqKGv9icD5kK8dTdsQqHlu7CA8SLgUCVNhmecrLf0sbtn7++ed0FSN6FkKsKmLlsZqC7ykU8c8//+w5Wx5ZalFpTE7LitTauuyyy1xEU3nOa4BeM4u0uMrD1uVSC8TKY0mNWTVr1iyYAXZPFaqdJUFSeBpFRX3ppZec86k85ps3b2433nijDRgwwLlJqOWleFwkCNQUAcTKQ74Ultt4inVAsjTOpbGsb775xsWP1yC9NnCVeMmfS8t/tFZRXvWagSRB4EARQKw8pJOWVU0sZPYUp0az1PLS7KIinE6ePNnFkr/99ttdy1PipRDNjz/+uH355ZfuOrzpa9RcZf3jiJXHvHK2XLhwYVmPWXmqXe0sCZIcZhMvei39UZQKDdorSsTQoUNt0qRJzmFV25n9+eefbvCeMbBqI+ZCDwHEygOFrOwJKJb8nDlzbMqUKS6AoLYf01IgDdxr/8TRo0e7buUnn3xiCuvMZhnZM479DsTK8wRoNlBdHnV/SNkTkBDJOVXLljSrOn78eOdNr1lHrQy4/PLL3S4/gwYNcpxfeeUVU7RURbtQq5YEAR8BxMpDRWNWahksWrTIc5asXAjIa15c1S1cvHixE7BRo0bZfffd55YGaXmQupNaKqQZSM1MSuiWLFniBvzVGmM2Mhfy5XMPYuWxpf6oNPtV6K24PD8VfZbcJuRlL78urWMcO3as87DXgmwtJpeIScA6dOhgnTt3tjFjxrixMm3ooUF9dT81hoaQlf+jhFh5bKzuSMeOHV2sKM9psg4AAQ3Ka7nTF1984XYaev75553bhMa/tNaxRYsW7qUZSYlYr169bNy4cU7INC4m8VNUVW0uq269xIwB/gNguCL+BGJVRLh8dXEISHy0mYe6k9pz8bnnnnOtsfbt27vAhFdeeaWbmZSgderUyQnZ4MGD3QC/QkPLwVVOsOpa6rs0vqZxNsSsOPYq1LciVoUiyfeUDAF1LT/99FMXZUILtjXAr5aXWmRamaBZyksuucQkanJ41Z6Nw4YNc/5iGivTWKUG/CVoLPQuGbOyu43PFJrFatmyZckH3/OVnbzKBNRiUutJM43qXmpMUuNd8qV7+eWX3fpIhYiWaKlbqeVGEjJNsmixt54FtdAUH0xdTXVJZ82a5Z6P1atXO38yDR0Qeqcy+0Lm0LLy0NTDrP/ApR4p1FN0snIkICHTQH0yY6klR2qdJYImL325WshjX2NkrVu3dq0yzWBqEkCTAfLsVxSLvn37uokAdU9nz57ttnTTOJpaa5pM2LJli/stup3ZGQux8vBKxIrlNh44kWdJ1PR8SMzWrVtnallpKZLcLOQQK1HT+kl58msMTbskaTZT3U35manVpjzNbnbp0sXtxK0u6JNPPulaeRqD0xZsEjbtYCRfP814bt261S04j7n1hlh5/vj0H1a7yOhhzEx6WPSfUf5CybseJHUvSBBIE9AzoWdEralE1NRS0yD/1KlT3YD/iBEjXGBEtcwkanqXoClQot4lcsrXLKgEUC07TRYkKwJeeOEFJ5Rys9FvSET1bOqZ1HCGZkP1PCcTCenyhXaMWGVpMT0Up512mp100kl28sknW/369e3MM8903UY19UkQyJWAWm0SGLWk1LJatmyZvfXWW258TOKmHYw0ZjZkyBDr0aOHG1/TjKfWZGqMTUubtDpAY23qnqpbqlbcPffc47qmEjltLjJx4kS3cmD69On2xhtvuFnVtWvXulacJic0vpe85PKhl2ZLa3rGFLHyPFn6j6jxKv2HykwaXD333HNtxYoVe196qDQwe8YZZ2RezmcIFJ2AWvtqQcmvTKKjf5pqvWlmU1FgNRuq7qlacZpI6Natm9sNSS03CV3jxo3dDGkyS6p35WtiQYLXpk0b16rTyoKkRacur2ZaNdGgLrBajPqbWblypeuRKHBloR11ESvPo6QxCXmwy48nM2kDBu2OnJlkrHr16mVm8xkCNU5AA/l6STzUYlKXUP+Q1T1US0pdRrlpaFs3dSX1z1ctLrXm1ArTqoKRI0e6Fp0mGRTDXy07TSbIHURBGiVuatHppWNF4VCrL5mAUHdWrTw5W0ss9T2PPvqo6wrrdxTBY38JsfIQklhVtRXXKaec4v6bpG/TQKhmhNQMJ0GgHAkkYqeuajJzqi6reh/qtmoiQCsO9LewatUqN5OqiQcFalTLSyGDJE5y/9AeAJoxVWBHvSR8Go/bX0KsPISqEis1s4866ig766yz7MILL9z7Ou+885yTocYZSBCAQPUIJONi6sZqNcH+EmLlIaT/HPJiztwwQuMA55xzjmu6yodmwoQJVrt2bdc8jnlK2YOQLAgUnABilQVS+cJotkX/EZK0YMECO/vss+3HH39MsniHAAQ8BNRd1IykzyXIc3mlLMSqEhJzA5Ca1s0MvqdZEW1VlZlOP/1055eVmc9nCEDg/who0F3DJ/IZu+OOO3KaKUSsPE+Txqw0q5EZfK9BgwY2b968SneoS9iwYUM3fVzpJBkQgIDzTdQgu3olmoXMJSFWHmoSK027ZoqVBEzeyJlJPi6alpXvFQkCEKhMQL0PzQrmk6oUK01VaqmApiHVHZL3qi9pClK+GuWUJFZylMsUq3KqI3WBwIEkIIfp6vhS7atMVYqVujvnn3++HXbYYXbiiSfaI488UmFgOfnSchUrrc0i6kJiZd4hkB+BoomVdtqVN7ZWj8v/QYp48MEH2/LlyyuVuFzFytcNrFR5MiAAgWoRKJpYaSCsUaNGFYKJyeu0Xbt2lQpWjmKllevHHHOMaYsoEgQgkD8BRWaVN3s6KfCh/taqm7zdQDk7aswmnbSAUQHpMlM5ipUG0SVWWrNEggAE8ieg9Ydytk4nxe3q3bt3Jefr9DXpY69YaZV2plg9/PDDbnFi+mYdl6NYSe3r1KmDWGUam88QKDABLZqWYPkinGT+VN5iJScveaVqw8pyeWmsTsto5LxWLnWiHuXzfJabLaUh2tBjf8krVoqBoz6m3BeSNHToUBe1MPmcvCvIvhbwyr2hXF7aTKBJkyY2Y8aMsqlTudiGepTP35lsqf0dFXFBcbH2l7xipY0l5cSVxHOS06Nc5TXwnpnKsRuYOIWyI3OmtfkMgcIRUEwt9cqqI1T6Va9YqUWl7buPOOIIu+iii+zoo492YVMVvyYzlbNY4RSaaW0+Q6BwBMaMGeM2qU334Pb17V6x0g1SPQXPUkB6OYj6hErXIVb7wss5CECgKgKaIaxqZYzvnirFynexLy8tVvphjfeo+6g916oTUMv3nTWdl3QD8WCvaUvw+xD4fwIFEysJlfyzjjvuODftX7duXVO88hAFS4H0VBfFpSZBAAKlQaBgYqX4yyeccIIbLFMfVLtsaFBeXqokCEAAAvkSKJhYaZtszSCmkwLVKWAdCQIQgEC+BAomVvJw1/bY6aStsBWxgQQBCEAgXwIFEyttgKg9xNJpyZIlbjeYdB7HEIAABHIhUDCx0rbU2sgwnbTx56mnnprO4hgCEIBATgQKJlbapkpjVmm/CS1Q7NChQ04F4yYIQAACaQIFEyuFVTn++ONt2rRpbk2hZgMVwG/y5Mnp3+MYAhCAQE4ECiZW+vUpU6bYIYccYrVq1bKDDjrIOnfunNOWOznVhJsgAIGyJlBQsZJ/lbZYVzwobWiYGWyrrElSOQhAoKgECipWRS0pXw4BCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEMhbrMKpKiWFAARCJoBYhWw9yg6BiAggVhEZm6pCIGQC/wN+Jc0npxG4UgAAAABJRU5ErkJggg=="></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mfrac><mi>W</mi><mi>q</mi></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>16</mn></mrow></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>60</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></mrow></mfrac><mo>=</mo><mo>»</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">V</mi><mo>»</mo></math> <span class="fontstyle0">✓</span></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mi>Q</mi><mo>×</mo><mfenced><mrow><mfrac><mn>1</mn><mrow><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfrac></mrow></mfenced><mo>=</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></math> ✓</span></p>
<p><span class="fontstyle0"><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>8</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">C</mi><mo>»</mo></math> ✓</span></p>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">to highlight similarities between </span><span class="fontstyle2">«</span><span class="fontstyle0">different</span><span class="fontstyle2">» </span><span class="fontstyle0">fields </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The majority who answered in terms of potential gained one mark. Often the answers were in terms of work done rather than work done per unit charge or missed the fact that the potential is positive.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was well answered.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most didn't realise that the key to the answer is the definition of potential or potential difference and tried to answer using one of the formulae in the data booklet, but incorrectly.</p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Even though many were able to choose the appropriate formula from the data booklet they were often hampered in their use of the formula by incorrect techniques when using fractions.</p>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered with only a small number of answers suggesting greater international cooperation.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the gravitational field lines of planet X.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how this diagram shows that the gravitational field strength of planet X decreases with distance from the surface.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The diagram shows part of the surface of planet X. The gravitational potential at the surface of planet X is –3<em>V</em> and the gravitational potential at point Y is –<em>V</em>.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Sketch on the grid the equipotential surface corresponding to a gravitational potential of –2<em>V</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A meteorite, very far from planet X begins to fall to the surface with a negligibly small initial speed. The mass of planet X is 3.1 × 10<sup>21</sup> kg and its radius is 1.2 × 10<sup>6</sup> m. The planet has no atmosphere. Calculate the speed at which the meteorite will hit the surface.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At the instant of impact the meteorite which is made of ice has a temperature of 0 °C. Assume that all the kinetic energy at impact gets transferred into internal energy in the meteorite. Calculate the percentage of the meteorite’s mass that melts. The specific latent heat of fusion of ice is 3.3 × 10<sup>5</sup> J kg<sup>–1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the field lines/arrows are further apart at greater distances from the surface</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>circle centred on Planet X<br>three units from Planet X centre</p>
<p><img 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"></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>loss in gravitational potential = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{6.67 \times {{10}^{ - 11}} \times 3.1 \times {{10}^{21}}}}{{1.2 \times {{10}^6}}}">
<mfrac>
<mrow>
<mn>6.67</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>11</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>3.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>21</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>6</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>«= 1.72 × 10<sup>5</sup> JKg<sup>−1</sup>»</p>
<p>equate to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>v</em><sup>2</sup></p>
<p>v = 590 «m s<sup>−1</sup>»</p>
<p> </p>
<p><em>Allow ECF from MP1.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>available energy to melt one kg 1.72 × 10<sup>5</sup> «J»</p>
<p>fraction that melts is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.72 \times {{10}^5}}}{{3.3 \times {{10}^5}}}">
<mfrac>
<mrow>
<mn>1.72</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>3.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> = 0.52 <em><strong>OR</strong></em> 52%</p>
<p> </p>
<p><em>Allow ECF from MP1.</em></p>
<p><em>Allow 53% from use of 590 ms<sup>-1</sup>.</em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the Earth-Sun distance.</p>
</div>
<div class="specification">
<p>The molar mass of nitrogen is 28 g mol<sup>−1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the intensity of the solar radiation at the location of Titan is 16 W m<sup>−2</sup>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the <strong>average </strong>intensity of solar radiation <strong>absorbed</strong> by the whole surface of Titan is 3.1 W m<sup>−2</sup>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the equilibrium surface temperature of Titan is about 90 K.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The mass of Titan is 0.025 times the mass of the Earth and its radius is 0.404 times the radius of the Earth. The escape speed from Earth is 11.2 km s<sup>−1</sup>. Show that the escape speed from Titan is 2.8 km s<sup>−1</sup>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The orbital radius of Titan around Saturn is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> and the period of revolution is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>T</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant="normal">π</mi><mn>2</mn></msup><msup><mi>R</mi><mrow><mo> </mo><mn>3</mn></mrow></msup></mrow><mrow><mi>G</mi><mi>M</mi></mrow></mfrac></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math> is the mass of Saturn.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The orbital radius of Titan around Saturn is 1.2 × 10<sup>9 </sup>m and the orbital period is 15.9 days. Estimate the mass of Saturn.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the mass of a nitrogen molecule is 4.7 × 10<sup>−26</sup> kg.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the root mean square speed of nitrogen molecules in the Titan atmosphere. Assume an atmosphere temperature of 90 K.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss, by reference to the answer in (b), whether it is likely that Titan will lose its atmosphere of nitrogen.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>incident intensity <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1360</mn><mrow><mn>9</mn><mo>.</mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfrac></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>7</mn><mo>≈</mo><mn>16</mn></math> «W m<sup>−2</sup>» ✓</p>
<p> </p>
<p><em>Allow the use of 1400 for the solar constant.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>exposed surface is ¼ of the total surface ✓</p>
<p>absorbed intensity = (1−0.22) × incident intensity ✓</p>
<p>0.78 × 0.25 × 15.7 <em><strong>OR </strong> </em>3.07 «W m<sup>−2</sup>» ✓</p>
<p> </p>
<p><em>Allow 3.06 from rounding and 3.12 if they use 16</em> W m<sup>−2</sup>.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>σT </em><sup>4</sup> = 3.07</p>
<p><em><strong>OR</strong></em></p>
<p><em>T</em> = 86 «K» ✓</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>«</mo><msqrt><mfrac><mrow><mn>2</mn><mi>G</mi><mi>M</mi></mrow><mi>R</mi></mfrac></msqrt><mo>=</mo><mo>»</mo><msqrt><mfrac><mrow><mn>0</mn><mo>.</mo><mn>025</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>404</mn></mrow></mfrac></msqrt><mo>×</mo><mn>11</mn><mo>.</mo><mn>2</mn></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>79</mn></math> «km s<sup>−1</sup>» ✓</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct equating of gravitational force / acceleration to centripetal force / acceleration ✓</p>
<p>correct rearrangement to reach the expression given ✓</p>
<p> </p>
<p><em>Allow use of <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mi>G</mi><mi>M</mi></mrow><mi>R</mi></mfrac></msqrt><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mi>R</mi></mrow><mi>T</mi></mfrac></math> for <strong>MP1</strong>.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>15</mn><mo>.</mo><mn>9</mn><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></math> «s» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant="normal">π</mi><mn>2</mn></msup><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfenced><mn>3</mn></msup></mrow><mrow><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>×</mo><msup><mfenced><mrow><mn>15</mn><mo>.</mo><mn>9</mn><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></mrow></mfenced><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mn>5</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>26</mn></msup><mo> </mo></math>«kg» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mn>28</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow><mrow><mn>6</mn><mo>.</mo><mn>02</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup></mrow></mfrac></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>65</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>26</mn></mrow></msup></math> «kg» ✓</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mi>k</mi><mi>T</mi><mo>⇒</mo><mo>»</mo><mi>v</mi><mo>=</mo><msqrt><mfrac><mrow><mn>3</mn><mi>k</mi><mi>T</mi></mrow><mi>m</mi></mfrac></msqrt></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>«</mo><msqrt><mfrac><mrow><mn>3</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>×</mo><mn>90</mn></mrow><mrow><mn>4</mn><mo>.</mo><mn>651</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>26</mn></mrow></msup></mrow></mfrac></msqrt><mo>=</mo><mo>»</mo><mn>283</mn><mo>≈</mo><mn>300</mn></math> «ms<sup>−1</sup>» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow 282 from a rounded mass.</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>no, molecular speeds much less than escape speed ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from incorrect <strong>(d)(ii)</strong>.</em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A vertical wall carries a uniform positive charge on its surface. This produces a uniform horizontal electric field perpendicular to the wall. A small, positively-charged ball is suspended in equilibrium from the vertical wall by a thread of negligible mass.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The centre of the ball, still carrying a charge of 1.2 × 10<sup>−6 </sup>C, is now placed 0.40 m from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.</p>
<p>P is the point on the line joining the charges where the electric field strength is zero. The distance PQ is 0.22 m.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The charge per unit area on the surface of the wall is<em> σ</em>. It can be shown that the electric field strength <em>E</em> due to the charge on the wall is given by the equation</p>
<p style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mi>σ</mi><mrow><mn>2</mn><msub><mi>ε</mi><mn>0</mn></msub></mrow></mfrac></math>.</p>
<p>Demonstrate that the units of the quantities in this equation are consistent.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.</p>
<p>Determine the horizontal force that acts on the ball.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The charge on the ball is 1.2 × 10<sup>−6 </sup>C. Determine <em>σ</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The thread breaks. Explain the initial subsequent motion of the ball.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the charge on Q. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, without calculation, whether or not the electric potential at P is zero.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>identifies units of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math> as <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>C m</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>C</mi><msup><mi>m</mi><mn>2</mn></msup></mfrac><mo>×</mo><mfrac><mrow><mi>N</mi><msup><mi>m</mi><mn>2</mn></msup></mrow><msup><mi>C</mi><mn>2</mn></msup></mfrac></math> seen and reduced to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>N C</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> <strong>✓</strong></p>
<p> </p>
<p><em>Accept any analysis (eg dimensional) that yields answer correctly</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontal force <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> on ball <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>T</mi><mo> </mo><mi>sin</mi><mo> </mo><mn>30</mn></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mrow><mi>cos</mi><mo> </mo><mn>30</mn></mrow></mfrac></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo> </mo><mo>«</mo><mo>=</mo><mi>m</mi><mi>g</mi><mo> </mo><mi>tan</mi><mo> </mo><mn>30</mn><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>025</mn><mo>×</mo><mo> </mo><mn>9</mn><mo>.</mo><mn>8</mn><mo> </mo><mo>×</mo><mi>tan</mi><mo> </mo><mn>30</mn><mo>»</mo><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>14</mn><mo> </mo><mo>«</mo><mtext>N</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p><em><br>Allow g = 10 N kg<sup>−1</sup></em></p>
<p><em>Award <strong>[3] marks</strong> for a bald correct answer.</em></p>
<p><em>Award <strong>[1max]</strong> for an answer of zero, interpreting that the horizontal force refers to the horizontal component of the net force.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>14</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>«</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo>»</mo></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>85</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>12</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>14</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>»</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mo>«</mo><msup><mtext>C m</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>
<p><em> <br>Allow <strong>ECF</strong> from the calculated F in (b)(i)</em></p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontal/repulsive force and vertical force/pull of gravity act on the ball <strong>✓</strong></p>
<p>so ball has constant acceleration/constant net force <strong>✓</strong></p>
<p>motion is in a straight line <strong>✓</strong></p>
<p>at 30° to vertical away from wall/along original line of thread <strong>✓</strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>Q</mi><mrow><mn>0</mn><mo>.</mo><msup><mn>22</mn><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>18</mn><mn>2</mn></msup></mrow></mfrac></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>+</mo><mo>»</mo><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mo>«</mo><mtext>C</mtext><mo>»</mo></math><strong>✓</strong></p>
<p>2sf<strong> ✓</strong></p>
<p><em><br>Do not award <strong>MP2</strong> if charge is negative </em></p>
<p><em>Any answer given to 2 sig figs scores <strong>MP3</strong></em></p>
<p> </p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>work must be done to move a «positive» charge from infinity to P «as both charges are positive»<br><em><strong>OR</strong></em><br>reference to both potentials positive and added<br><em><strong>OR</strong></em><br>identifies field as gradient of potential and with zero value <strong>✓</strong></p>
<p>therefore, point P is at a positive / non-zero potential<strong> ✓</strong></p>
<p><em><br>Award <strong>[0]</strong> for bald answer that P has non-zero potential</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A conducting sphere has radius 48 cm. The electric potential on the surface of the sphere is 3.4 × 10<sup>5</sup> V.</p>
</div>
<div class="specification">
<p>The sphere is connected by a long conducting wire to a second conducting sphere of radius 24 cm. The second sphere is initially uncharged.</p>
<p style="text-align: center;"> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZgAAACJCAYAAAARxi7fAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABuqSURBVHhe7d0LVFV1vgfw7zDdatRIJcWKEFEGhQlRE0uqidKRBcYlnVFztLDUNWaROq6r+Gi1MkHnusBIskEnyczXDeVSsnyGo6KFiaRLlPCBpAaaqYRO0yru3b8/e8vxRXA4j70P30/LBXtz2GefveP/2//f//Wr/9OAiIjIwbz0r0RERA7FAENERE7BAENERE7BAENERE7BAENERE7BAENERE7BAENERE7BAENERE7BAENERE7RIkfyl5WV4dy5czh79ixKS0tx6dIltX/FiuXqa0NiY59Gu3btcPfddyM4OBgdO3ZEhw4dEBQUpL+CiIiExweY7777DkeOHMGXX36JAwcOYMOGj/Hww/3RrVs3REREoE2b1ujcOUC91s/PD7/5zW/U9zfzr3/9C6dOnVLfnzxZjpqayypAlZeXXz1uVFSUFmy6oUePENx///3qtURELZFHBhgJJgcPHkRubi6qqioRExOrahuhoaFOrWlIzUgCz759RcjL2wBf304q4PTv3x89e/bUX0VE1DJ4TIA5ffq0CiirV69SBXtcXBz69evn1tSVnFN+fv7VQDdixLMYMGAA02lE1CJYOsBIyqqgYBcyM5eoAnzcuPGqxmDG1JRtsBHjx49DZOSjDabkiIiszJIBRgLLpk2bkJaWqgrpwYMHqzSUVUgKb82aNSo4Sq1m+PDhaN++vf5TIiLPYKkAYwSWxMSXMXHiKxgyZIil001GWi8lZS6SkmYy0BCRR7HEOBgJLDk5OYiOHoTCwkIUFx/AtGnTLN+WIam8CRMmqM8jnnkmXn1O+bxERFZn+hqMpJPmzp0LHx8fTJkyxaMbyKUX2rJly3D06FHMnDmTPc+IyNJMG2DkKT49PV119509ezYGDBio/8Tz7d69G0lJ01X70tSpU5k2IyJLMmWKTGotkg4TGzdualHBRUiHBfncMluApM0k4BARWY2pajBSa8nKylJjWdLT32aKSCPBNjHxFTVYNDExkd2aicgyTFODkSldpI1FpnNZvz6HwUUn10FqMzJfmlwf6XlGRGQFpggw0rgtqaCwsDAsXryYbQ7XkVpLcnIyIiMjMXLks6pWQ0Rkdm5PkUn7wogRw7B69VpLDZZ0F6MDQErKPF4vIjI1twaYrVu3YM6cOVi69B+cn6sJJE0mNRmZBUDG0RARmZHbAoykwqQxf+XKVZzW3g4MMkRkdm5pg2FwaT65btL4L50i5HoSEZmNywPMihUrGFwcRBr/U1NTGWSIyJRcGmCkgXrJkkwGFweSIDNr1iwVtGUeMyIis3BZgDF6PzG4OJ5cT7musnwBR/0TkVm4pJHfaJBm11rnkvFETz0VhW3b8tkrj4jczuk1GJn+ZfLkydq/KQwuTiZBRcYTjR37opoZgYjInZxeg5kxY4aatFHWbyHXkAZ/NvwTkbs5tQYjjc6ytolM0kiuk5CQoL5Kjz0iIndxWg1G2l0eeaQf9uz5nI36bmC0e3GWBCJyF6cFGBldPmjQIMTHx+t7yNVkKp7MzCV4//33Oc0/EbmcU1JkxngMBhf3koXaunXrhuzsbH0PEZHrOLwGI72XwsPD2FXWJIz7wVQlEbmaw2swCxYsQHLyPAYXk5C1ddLTFyEjI0PfQ0TkGg4NMDLQr6BgF4YOHarvITOQtjC5L1yojIhcyaEpMhnzEhERwbYXE5IpZBYuXIi1a9fqe4jI7KQ36OHDJaisrEJJSYka9vHZZzdOBxUb+zTatWuHkJAQBAYGonv37qZYGdhhAcYowNhjybyGDRuGSZMmcUYFIhOTTNDWrVvVBLYiJiYWwcHBCA0NRatWrW7aliq/c+XKFZw4cQKlpaXIy9sAX99OiIuLQ1RUlNvaXx0WYKRb8ujRo1l4mRhrMUTmZfx9CkcEBkmJyzElUEVGPorBgwe7vHx2SICR6CnzX/3znzv0PWRWrMUQmYsRWHx8fJzykC7zQe7fv/9q8Jo7d67LOmE5JMCw7cU65H/mTz75BMnJyfoeInIHGUIgvW6lXcVVD30y+HrOnDkq7SZTeDm7OaPZvcjkIq1YsVz1VCLz69Wrl+pRJo2HROQe8qD3zDPxqlFe2q1dlVGQwdey1LqIjh7k9J6lza7ByISK33//vWqDIWvgPSNyH5nlXNpF3D1PoAQ5WQRSllJxVvap2QHm979/nBMqWowxEaY8ybDHH5FrSFuIpKcuXLiA1NRUU/ztGWXBiBHPOuWBs1kpMqleSVc4BhdrkZ4pISGhquGPiJxPgsuUKVNMFVyElAXyoOms9aOaFWCkiiXd6ch6hg4dgp07d+pbRORMWVlZ6quZgotBzkfOS4KMo9eQalaKTNJjK1euctsgHrKfMQlmRcUpfQ8ROYMU2gUFBaYMLraMdFlKyjyHdTqwuwYjY18kPcbgYk0yjYRML8H5yYicR/6+lizJxKxZs0wdXISU5dKeLg3/juplaneAOXTokBppStYVGRmJgwcP6ltE5EjS7pKY+ArS09+2zIO4tKdLr7I333xT39M8dgeYwsJCjga3uH79+iE3N1ffIiJHknYXGdDYs2dPfY81GF2WjYUjm8PuNhh/fz+UlpaZvtpHDeN9JHI8Y/qs9etzTDGrcVMZ59/coQx21WDkzSV/z0LJ+kaNeg5fffWVvkVEjrBs2TKVarJicBGSKpOxMUbvN3vZFWCk/SUsLEzfIiuTqSpkim8icgxpIJfpmKw+fdbw4cORkjJXtSXZy64A880332gRrpu+RVYmixNJexoROYa0a44bN97yGR6pfU2c+IoKlvayK8B8/fXX6Nw5QN8iK+vQoYOazZWImk+e9mWesZiYGH2PtUVHRyMzc4m+1XR2BRiZPdnPz0/fIiuTXOvNlmAloqaT6ZdkGiartr1cT3rAVVVV2j0upskBxsjHsYHfczz8cH+HDawiaslkYKVMw+RJpLF/7969+lbTNDnAnDp1SvU8Is/RrVs3tZ43ETVPfn4+evQI0bc8g9Ri7G2ntStFRp7l7rvvxrlz5/QtIrKHzO8n6WZPmz6re/fuqlnEHk0OMCdPlqsCiTxHcHAwzp49q28RkT3Onz/vkdkdaU/q0iVQBdCmanKAqam5rAokIiKqJ+MDH3jgAX3Ls0RGPqoCaFMxRUZE5CD33nuv/p1nsTeNzgBDREQNsjeNzgBDROQApaWl6NKli75FosmzKRtTOBtTOpP1yT1dtWoV9uwp0PcQUVMFBnZFcnKKRy5jYm+5zwBDvKdEDuDJf0f2fjamyIiIqEGS/uvYsaO+1XgMMEREDlJTU6N/51kuXbqkJsZtqiYHmDZtWqvp+omIqF5oaChKSkr0Lc8iU/a3atVK32q8JgcYmaZfpusnz2Fv9ZeI6vn4+DRr7RSzkhH8J04ct2sKHKbIyO7qLxHVM6bo97SZyaVCYe8UOE0OMLIOjL0Tn5E5yYJj9lR/iehaMTGxOHzYs9Jku3fvRkREhL7VNE0OMMY6MM1Zp5nMxRNngCVyh8ceewzZ2ev0Lc8gSxD07dtX32oau1JksbFPq3VhyPqkOi8LjhFR8/Xq1QsbNnxs18zDZiQLqAl7H0DtCjABAQFq2n6yvpMnT6oFx4io+STDk5Q0Ezt27ND3WJukx0aOHKlvNZ1dAUYmPisrO6pvkZUdP37c7vwqEd1owIABSEtLtXwzgtTCUlLm4vHHH9f3NJ1dAUb6ex84cEDfIiuTfvtunaCvMgdj/f0QnlaEn/RdLY4zrkFNGbalLcLHlXLEn7S3eBn+/oOQVmSSgYAefN+DgoLU+imbNm3S91jTmjVrVG3M6B1nD7sCjPQkkzwjG/qtT3oEeuoiSS2XFlC2voUxaUfws9q+DZ3iF6GiYhMm926j9rhdp3gsrTiF4sm9tbPzPGPGjLF0LUbaZqX2Mnz4cH2PfewKMJJnlIb+r776St9DVlRWVqYa+JvzhEJEN5JajHRZzsrK0vdYS0ZGBtLTFzW7bLArwIjIyEgcPHhQ3yIrkiVeo6Ki9C2zqEbZ9izMjA6Gv7+f9i8CY9NyUFT5o/7zr5EzNgz+CanI+WAmotVrtH/RryGnrFp/jUaliF5ED/XzYETPXIS0sRHwD09F0S1zMj+isuhDm/eW3/uw/r21Y27PsnnPHi8iLacIlbV1P65L+4QhIW01Ppj5tM0xclBWY7yoVjvMlrpzUT9/GjNX7UF9n8xbpLNuSCnd6ly/Q1FaLCISZfbbHCRGBGi/8zm+vnrMalRvf027Ln9GVtkP6kh1fkBZ1p+1z/QatlfLuV5/fLkPW2w+h60a7T0H2fyu+BbbZz567b7aUmTFBaPHzO2ovubz6Pc0OgFjjfeLy0KZ9mu1lXttrqUfeoxNxzbb+2xi48aNw+rVq672xLKKrVu3qLFxgwYN0vfYz+4A069fP+Tm5upbZEWSIzbX2hU/4kzObMQ99w6qRqxDScUplBem4L5N0xCf8C6KbAu3T/+Od4/0xdslFdpr3kcC1iAxbkFdYVZbgZypf8aYTfcjZVsJKsrzMf3Xm5C2+Yz+yzejFfxF7yIh/g3si3gHheUVKNkyC37rtPcevxJlP9Ud87n55zFii3bMiuMoXNwFmxKfRcJbe7Ui1vAdPk37EEf6LtDOX3vN8tHABy8jLmWHFjq1dzmTi6lxL2OT7wxsU+c+Cb/elIOmDc1r6FxzcderG1CYLtOqxyO9sBzFk/vgP+p+UeMF795PYkjrL7Cu4KR2JF3tSRSs+wKthzyJ3t5ayFDHfwtVMcu04xv3QfscU3NxxuY21GmFbr36ofXlT7GlSO+eq12v/RvKAZt9tcf2YF3xHYjs2xXaW9xI5vGS+17+BXLfiEbXK3vxVsIoJFfFIrvwuHYfC7H4vi0YEzcbOWeMBw7zkqf/lJR5SEx8xTKpMkmNvfCCpPfSro55bA67A4xUAauqKj1uWoSWQnqISDvab3/7W32PCVTvRkZSNhAzA288FwppLfDqFIX/Sp6IkJIMvP5RWX2B2Ho4pk+LQ1AbL+01kRg94iGtMPsc+49e0QqyT/Fe3u0YPT0R8UFaUeZ1H56Y+leMbq3/7k19hy+y16JEjjs1Cp28vNAmeDSWHj6Fitzn4LtrKZLytFNLmYHngqV4vB2dnngZyZNDUJK2EB/Z1AZaj/4rpsUHa+evvebxP2FEeGtc3lCEoz/9gGOb/wd5sD33KEydPhwNntoNGjrXBAT90l+19+8wcEgHFK/bg2P6Ba0r/DtgyMDfwbu2DB+9noGS8Jcw7eX+2vHr7oOcJ/IWIGPHt3W/dJURtM7hYPl5dY9qTxxAvoorxj4tKJ4+jjI8iEdDbzUtUQQGazWYNl6dEB7eFsc+Woi0kocwbVoC+na6vf4+IhtJGbtVwDY7eYAbMeJZTJkyxfRBRs5v5Mhn8d57yxw28NruACPkwu3du1ffIispKtqHiRNfcchTiqPUVpXj4OXWCHq4hyrU6miFZ7cw9Gl9GWVl39TXFO5oC+9Wxotuw11t2+nfa4V4wRYUIxx9u7fV92lUoRqgb9yE8cQdFIj7tYL/Wj+iqvwYLiMID4d2tPmj8dae3B/UgsNJlJ2ur8PccY+39kyv82qFth3v0DfO4dCug0Bkb3T3No6iFc7deyNS32qUBs+1Mdqj98An0br4f/FJ8UVtW79mrZ/EwN7tgbOHsav4MtpHhaHL1cMb51mODfsrbuz55d0VfSPv0IOWfrzwcZj8rBbIdh3GWS0oFm35FJfDByKy6536L12nfSD87zGa/PVr1b4PwrrYvF69T3s9YOv7TG7ChAnqa3p6uvpqRhJcJAhKmT5gwEB9b/PZ83/nVRKdV65cqW+Rlch0FjKthZnUfv8dKnAHOrZtde3/mK28cY9WRl+uuogr+q5b+wnfX7j+CVvcCe97GlFP6NgWd93wV2Ecsx3a3mXb58lLO7W22hlXo+piI55OfzqHE1/cZIT3Pf4Itact9abn2hhGjWMvMrOLUX1NesxLuw8XtYCg1ZPS4hCot32ofxEvY3PdAW6iA0IffRAoO47TNdU4XVaJ8CH/iZgenYGCIhz5+ktsWXdO2/cIujbmnGuv4OLZf2snkYr4QJtz8H8EiZutN0o+NTUV5eXlWLx4sb7HPIzgEhYWdjUYOkqzAkzPnj2ZJrMgIz0m01qYiddd7eGPf+PsxSv1qTBxpRrfamVNa9+29TWDW9JqM+3u0b5ewMXvbR9xf0D1t5f17xvwxXGcueHJ+FbHrNVO7aJ2xt7wbduImuBtHdDlIakhXMT3th/w2wocsqfMvOm5NpJeo7u87lPs3berPj2m/cjrrrboqNXLwt/YhvKKU6i47t/Nuxbfia6RAxEubS5bt2jB5DZEhXVDkNp3DMf3HdZqpwHavvsbV+gYNb/wN7Gt/MZzqCiegt4W6t8smQIJMjJ+UApxs6TLpCxwVnARzQowQqpUbOy3lry8PDWAykzpMeHlG4AHJRX22eH6nlmSuz96APskdRZ0r2qXaZhe0F2XtkLNCezfd07fuInb/NErNgD490VUX7kmvGluh29AV63ILcNnh87aBL9qHN1/EJfRGUH3N2Z8ie1TvnGUWlQfKUKBvnVz172mwXNtLD1NdvlzrPr72vr0mOjYA4+G45o2GlFbloU4/2DEZZXaXIN6dffvHD7PfA/r0A+9umk1UbXvn3g9cZ72HnX7Gke/VsVbUHDMpreb3hPN6GVmJUaQkam2nn/+ebc/mMswhWeeiXdacBHNDjBxcXGqK57ZG7Co3pIlmWo6C9Px7o+JKUO1CJiM15YfUu0ttZX5+NuMDJSETMTrfwxq1P+wXl2fxAsxP+KDeel1XZdrz2D7395AWklDNZj2eGjoMIRcXoN5C/LrAlzNIWRJd+Ier6MofAxSYrRTS0rG8lJpXv4RldsXYUZaCUImT8Ifg27RrnANLfj94U+IwXuYMOVDlGpBRj7fgnlrtCBluA0dQx/SAuQhZL6zXn/NZ8hasdHmNQ2dq21X4TKcOHMWx8rO6gMubRlpskPYvPnQ1fRY3Y+64A8vRKN18TuYv2i3On5t5W4smv8Oihu6D3rnga9KSgHjeHqbibjmPX6Rfq204DR/fhb2Slfx2krsXfQ3zC8OweTX43+5M4MJSZCZNm2amt/rkUf6qS7BriZl9YoVKzB27Iuql5uzgoto9i2S3gYyLYInruTmiWTyOl/fTqoXoPncjvvi5yB3+UvwXT0EIf5+CIhIwplB85GT9Rf0bmyDtpc/4hd8iGWDTiPpqRD4B0Rh3s+RGB3SUBuMF9r0/guycl5Dn8KXEBHgB/+QIVjt+xKW507FE227qGMun+aD1QO1Y/oHImLCCQxKX4WsV/s2omZVx+u+OCzIXYbxeBsDQ/y1z7cQPw+KR4j+c+EVNBKZ2bMQWZBU95qof+Dn/gNtXvML5+p9Ozo+PBJT/3ABafERGJxVF6xvcLXjQ8DV9FgduQ//jfycV+GbN0YdPyBiDPJ8X/2F+6DXirT/6mubek3khvf4ZV73xeOd/PWY4bsBQyMCtfv4EIbmdcKMnMV4tbdNBw4Lio+Px549nyMzc4kq4KU24QoyJkdqTzJF1Pr1OU4fpvCr/9Po39tNCq2FCxdi7dq1+h4yq2HDhmHSpEkmG//iCjKYLxaJeAOFS+PRSd9L5G45OTlqWhl5UJcpZpzx8Cdl9CeffKIGULry798hlUzjZOVDkHkZ98ezg0utPlI9AmOvPrlXoyxnCd7dfCdiBvdGR7WPyBykNrNx4yY1q7mkreQhUFJnzV1TRtp4JBUmx5MKwODBg1UlwJV//w6pwQjWYsyvxdReaitRlLsS7ySlYrPRcBHyPN6YnoA/PhHU6HQWkTtIWbpz505kZLyt5nyUabkCAwPRoUOHW9ZupF1FFoGUdbpkKRVZhVJ6+EonLPl7lx6/7uCwACNabvrF/PgAQGQ90jYjcwYWFhbiwoULanjBrUgwkh5qsl6XLKlihnZWhwYYaUCSeXekume2LrAtHYM/EbmaQzv6STXMExba8TTSiOjj48PgQkQu5dAajJCGJenfLV3wHDVhGtlPGgplMNXSpf8waddkIvJUDq3BCAkqycnz1II15H4LFixQDX0MLkTkag4PMGLo0KGqv7U7RqlSPbn+MgA2ISFB30NE5DoOT5EZpPeD9OleuXIVU2VuYKTG0tPfdlsXRSJq2ZwWYIQ0LkuDv0zwxl5lriXTT0j/+VGjRul7iIhcyykpMoOMUBVZWVnqK7mGjN4VkqokInIXpwYYMXfuXDXbMqeRcQ25zjJb8qxZs1hrJCK3cmqKzCDtMU89FYVt2/LZm8mJpIu4rKnNdhciMgOn12CEBJXVq9eqRn+ufukcRnCZPXs2gwsRmYJLAoyQUeTjxo1XhWBzZwmla8lEd2+++aYa7zJgwEB9LxGRe7kkRWZr8eLFal1q9ixzDAkuzlxTm4jIXi6rwRikEJTCUApFLrPcPAwuRGRmLg8wwjbIsE3GPgwuRGR2bgkwwggy0ibDINM0cr1kXW0GFyIyM7cFGCGFo/R6kiAja8nQL5Mu33K94uLiGFyIyNRc3sh/MzI4MClpOiZPnnJ19D/dSCavfOGFMarLN9d2ISKzM0WAEZL2mTx5Mvr06YPExET2MLMh7S3p6enIy9vAyUOJyDLcmiKzJYXm+++/r76Pjh6kUkFUlxKT9pZLly6ppagZXIjIKkxTg7ElqaA5c+aogZkyYWNLrM1IrSU7OxszZkzHe+8t4wBKIrIc09RgbElhun59DkpKStTTe0vrAGDUWgoKCtTS0wwuRGRFpqzB2DI6AERGPoqpU6eiffv2+k88j0yhs2TJEtXWIr3rGFiIyMpMWYOxJb2lpO0hJCQE4eFhaqoZT5vLTNJh8rnk83l7e6vPy+BCRFZn+gAjpA1GVmYsLj6gtj0l0Mj5y+eQTg1CPp+MbWEPOiLyBJYIMAZJj0kBbBto5s+fb7keZ3K+Ro1FSHuTfC5PTv8RUctj+jaYhkgNYMeOHUhLS4WvbyeMHz8OvXv3MWVBLedaVLQPmZlLUFVVqXrIxcTEMKgQkceydICxJT3NNm7ciIyMtxEb+zSGDh2CHj1C3DpuxAgq2dnrsGHDx5g48RU89thjHIVPRC2CxwQYgzSY79+/Hzt37lS9saRmExUVpVZ57Ny5s1MDjgSUI0eOqGCXn5+vaioxMbEqqPTq1YttK0TUonhcgLmetHccOnQIhYWFKCjYhRMnjmPUqOdUr7Q2bdogNDRUvc7Pz69RAUAC2KlTp9T3ctyamho1XkeOLaQ7dUREhDquLBVNRNRSeXyAuZ7UMs6fP39NcLhw4YJKYdnq0iVQBQsjKNmSFFy7du3wwAMP4N5779Ve20V9z/YUIqJ6LS7ANJYRiHx8fBg4iIjswABDREROYalxMEREZB0MMERE5BQMMERE5BQMMERE5BQMMERE5BQMMERE5BQMMERE5ATA/wNO+T0akSC8xAAAAABJRU5ErkJggg=="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the charge on the surface of the sphere is +18 μC.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe, in terms of electron flow, how the smaller sphere becomes charged.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Predict the charge on each sphere.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mi>V</mi><mi>R</mi></mrow><mi>k</mi></mfrac><mo>=</mo><mo>»</mo><mfrac><mrow><mn>3</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>48</mn></mrow><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfrac></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mn>18</mn><mo>.</mo><mn>2</mn></math> «μC» ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>electrons leave the small sphere «making it positively charged» ✓</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mfrac><msub><mi>q</mi><mn>1</mn></msub><mn>48</mn></mfrac><mo>=</mo><mi>k</mi><mfrac><msub><mi>q</mi><mn>2</mn></msub><mn>24</mn></mfrac><mo>⇒</mo><msub><mi>q</mi><mn>1</mn></msub><mo>=</mo><mn>2</mn><msub><mi>q</mi><mn>2</mn></msub></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>q</mi><mn>1</mn></msub><mo>+</mo><msub><mi>q</mi><mn>2</mn></msub><mo>=</mo><mn>18</mn></math> ✓</p>
<p>so <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>q</mi><mn>1</mn></msub><mo>=</mo><mn>12</mn></math> «μC», <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>q</mi><mn>2</mn></msub><mo>=</mo><mn>6</mn><mo>.</mo><mn>0</mn></math> «μC» ✓</p>
<p> </p>
<p><em>Award <strong>[3]</strong> marks for a bald correct answer.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A planet of mass <em>m</em> is in a circular orbit around a star. The gravitational potential due to the star at the position of the planet is <em>V</em>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Show that the total energy of the planet is given by the equation shown.</span></p>
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="E = \frac{1}{2}mV">
<mi>E</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<mi>V</mi>
</math></span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Suppose the star could contract to half its original radius without any loss of mass. Discuss the effect, if any, this has on the total energy of the planet.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The diagram shows some of the electric field lines for two fixed, charged particles X and Y.</span></p>
<p><span style="background-color:#ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">The magnitude of the charge on X is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Q">
<mi>Q</mi>
</math></span> and that on Y is <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span></span>. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.</span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">At P the electric field is zero. Determine, to <strong>one</strong> significant figure, the ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{Q}{q}">
<mfrac>
<mi>Q</mi>
<mi>q</mi>
</mfrac>
</math></span>.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="E = \frac{1}{2}m\frac{{GM}}{r} - \frac{{GMm}}{r} = - \frac{1}{2}\frac{{GMm}}{r}">
<mi>E</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mi>r</mi>
</mfrac>
<mo>−</mo>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
<mi>m</mi>
</mrow>
<mi>r</mi>
</mfrac>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
<mi>m</mi>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">comparison with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = - \frac{{GM}}{r}">
<mi>V</mi>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">«to give answer»</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"> </p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em><strong>ALTERNATIVE 1</strong></em><br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">«at the position of the planet» the potential depends only on the mass of the star /does not depend on the radius of the star ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">the potential will not change and so the energy will not change ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em><strong>ALTERNATIVE 2</strong></em><br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">r / distance between the centres of the objects / orbital radius remains unchanged ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">since <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{E_{Total}} = - \frac{1}{2}\frac{{GMm}}{r}">
<mrow>
<msub>
<mi>E</mi>
<mrow>
<mi>T</mi>
<mi>o</mi>
<mi>t</mi>
<mi>a</mi>
<mi>l</mi>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
<mi>m</mi>
</mrow>
<mi>r</mi>
</mfrac>
</math></span>, energy will not change <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"> </p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{kQ}}{{{{(0.600 + 0.820)}^2}}} = \frac{{kq}}{{{{0.820}^2}}}">
<mfrac>
<mrow>
<mi>k</mi>
<mi>Q</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>0.600</mn>
<mo>+</mo>
<mn>0.820</mn>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mi>k</mi>
<mi>q</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mn>0.820</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{Q}{q} = « \frac{{{{(0.600 + 0.820)}^2}}}{{{{0.820}^2}}} = 2.9988 \approx » 3">
<mfrac>
<mi>Q</mi>
<mi>q</mi>
</mfrac>
<mo>=</mo>
<mrow>
<mo>«</mo>
</mrow>
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>0.600</mn>
<mo>+</mo>
<mn>0.820</mn>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mn>0.820</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>2.9988</mn>
<mo>≈</mo>
<mrow>
<mo>»</mo>
</mrow>
<mn>3</mn>
</math></span> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"> </p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered but with candidates sometimes getting in to trouble over negative signs but otherwise producing well-presented answers.</p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A large number of candidates thought that the total energy of the planet would change, mostly double.</p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The majority of candidates had an idea of the basic technique here but it was surprisingly common to see the squared missing from the expression for field strengths.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span> is formed when a nucleus of deuterium (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{1}^{2}{\text{H}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msubsup>
<mrow>
<mtext>H</mtext>
</mrow>
</math></span>) collides with a nucleus of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{31}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>31</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span>. The radius of a deuterium nucleus is 1.5 fm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State how the density of a nucleus varies with the number of nucleons in the nucleus.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the nuclear radius of phosphorus-31 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{31}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>31</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span>) is about 4 fm.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the maximum distance between the centres of the nuclei for which the production of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span> is likely to occur.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, in J, the minimum initial kinetic energy that the deuterium nucleus must have in order to produce <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span>. Assume that the phosphorus nucleus is stationary throughout the interaction and that only electrostatic forces act.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span> undergoes beta-minus (β<sup>–</sup>) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by decay constant.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In a fresh pure sample of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span> the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s<sup>–1</sup>, the decay constant of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>it is constant ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>R</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{1}}{\text{.20}} \times {10^{ - 15}} \times {31^{\frac{1}{3}}} = 3.8 \times {10^{ - 15}}">
<mrow>
<mtext>1</mtext>
</mrow>
<mrow>
<mtext>.20</mtext>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>15</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>31</mn>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>3.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>15</mn>
</mrow>
</msup>
</mrow>
</math></span> «m» ✔</p>
<p><em>Must see working and answer to at least 2SF</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>separation for interaction = 5.3 <em><strong>or</strong></em> 5.5 «fm» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>energy required = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{15{e^2}}}{{4\pi {\varepsilon _0} \times 5.3 \times {{10}^{ - 15}}}}">
<mfrac>
<mrow>
<mn>15</mn>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mi>π</mi>
<mrow>
<msub>
<mi>ε</mi>
<mn>0</mn>
</msub>
</mrow>
<mo>×</mo>
<mn>5.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>15</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> ✔</p>
<p>= 6.5 / 6.6 ×10<sup>−13</sup> <em><strong>OR</strong></em> 6.3 ×10<sup>−13 </sup>«J» ✔</p>
<p> </p>
<p><em>Allow ecf from (b)(i)</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«electron» <span style="text-decoration: underline;">antineutrino</span> also emitted ✔</p>
<p>energy split between electron and «anti»neutrino ✔</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>probability of decay of a nucleus ✔</p>
<p><em><strong>OR</strong></em></p>
<p>the fraction of the number of nuclei that decay</p>
<p>in one/the next second</p>
<p><strong>OR</strong></p>
<p>per unit time ✔</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1 week = 6.05 × 10<sup>5</sup> «s»</p>
<p>17 = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="24{{\text{e}}^{ - \lambda \times 6.1 \times {{10}^5}}}">
<mn>24</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>λ</mi>
<mo>×</mo>
<mn>6.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
</mrow>
</msup>
</mrow>
</math></span> ✔</p>
<p>5.7 × 10<sup>−7 </sup>«s<sup>–1</sup>» ✔<br><br></p>
<p><em>Award<strong> [2 max]</strong> if answer is not in seconds</em></p>
<p><em>If answer <strong>not</strong> in seconds and <strong>no</strong> unit quoted award<strong> [1 max]</strong> for correct substitution into equation (MP2)</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">In a classical model of the singly-ionized helium atom, a single electron orbits the nucleus in a circular orbit of radius <em>r</em>.</span></p>
<p><span style="background-color: #ffffff;"><img style="margin-right: auto; margin-left: auto; display: block;" 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" width="249" height="248"></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The Bohr model for hydrogen can be applied to the singly-ionized helium atom. In this model the radius<em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></em>, in m, of the orbit of the electron is given by<em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>–</mo><mn>11</mn></mrow></msup><mo>×</mo><msup><mi>n</mi><mn>2</mn></msup></math></em> where <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></em> is a positive integer.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Show that the speed <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></em> of the electron with mass <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></em>, is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mrow><mi>m</mi><mi>r</mi></mrow></mfrac></msqrt></math>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Hence, deduce that the total energy of the electron is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>TOT</mi></msub><mo>=</mo><mo>-</mo><mfrac><mrow><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">In this model the electron loses energy by emitting electromagnetic waves. Describe the predicted effect of this emission on the orbital radius of the electron.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Show that the de Broglie wavelength<em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math></em> of the electron in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>3</mn></math> state is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup></math> m.<br></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The formula for the de Broglie wavelength of a particle is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mi>h</mi><mrow><mi>m</mi><mi>v</mi></mrow></mfrac></math>.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Estimate for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>3</mn></math>, the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>circumference</mi><mo> </mo><mi>of</mi><mo> </mo><mi>orbit</mi></mrow><mrow><mi>de</mi><mo> </mo><mi>Broglie</mi><mo> </mo><mi>wavelength</mi><mo> </mo><mi>of</mi><mo> </mo><mi>electron</mi></mrow></mfrac></math>.</span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">State your answer to one significant figure.</span></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">The description of the electron is different in the Schrodinger theory than in the Bohr model. Compare and contrast the description of the electron according to the Bohr model and to the Schrodinger theory.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">equating centripetal to electrical force <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><msup><mi>r</mi><mn>2</mn></msup></mfrac><mo>=</mo><mfrac><mrow><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math> to get result ✔</span></p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">uses (a)(i) to state <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi mathvariant="normal">k</mi></msub><mo>=</mo><mfrac><mrow><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math> <em><strong>OR </strong></em>states <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi mathvariant="normal">p</mi></msub><mo>=</mo><mo>-</mo><mfrac><mrow><mn>2</mn><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math> ✔</span></p>
<p><span style="background-color: #ffffff;">adds « <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>TOT</mi></msub><mo>=</mo><msub><mi>E</mi><mi mathvariant="normal">k</mi></msub><mo>+</mo><msub><mi>E</mi><mi mathvariant="normal">p</mi></msub><mo>=</mo><mfrac><mrow><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac><mo>-</mo><mfrac><mrow><mn>2</mn><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math>» to get the result ✔</span></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">the total energy decreases<br><em><strong>OR</strong></em><br>by reference to <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>TOT</mi></msub><mo>=</mo><mo>-</mo><mfrac><mrow><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math> ✔</span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">the radius must also decrease ✔</span></span></p>
<p><em><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">NOTE: <span style="background-color: #ffffff;">Award <strong>[0]</strong> for an answer concluding that radius increases</span></span></span></em></p>
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>3</mn><mo>,</mo><mo> </mo><mi>v</mi><mo>=</mo><mo>«</mo><msqrt><mfrac><mrow><mn>2</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></mrow></mfenced><mn>2</mn></msup></mrow><mrow><mn>9</mn><mo>.</mo><mn>11</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup><mo>×</mo><mn>9</mn><mo>×</mo><mn>2</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup></mrow></mfrac></msqrt><mo>=</mo><mo>»</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>44</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo> </mo><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo> </mo><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math><span style="background-color: #ffffff;">✔</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>63</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup></mrow><mrow><mn>9</mn><mo>.</mo><mn>11</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>44</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac></math> <em><strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mn>5</mn><mo>.</mo><mn>05</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo>»</mo></math><span style="background-color: #ffffff;">✔</span></strong></em></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mstyle displaystyle="true"><mn>2</mn><mi>π</mi><mi>r</mi></mstyle><mstyle displaystyle="true"><mi>λ</mi></mstyle></mfrac><mo>=</mo><mo>«</mo><mfrac><mstyle displaystyle="true"><mn>2</mn><mi>π</mi><mo>×</mo><mn>9</mn><mo>×</mo><mn>2</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup></mstyle><mstyle displaystyle="true"><mn>5</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup></mstyle></mfrac><mo>=</mo><mn>2</mn><mo>.</mo><mn>99</mn><mo>»</mo><mo>≅</mo><mn>3</mn></math> <span style="background-color: #ffffff;">✔<br></span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Allow ECF from (b)(i)</span></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">reference to fixed orbits/specific radii <em><strong>OR</strong> </em>quantized angular momentum in Bohr model ✔<br></span></p>
<p><span style="background-color: #ffffff;">electron described by a wavefunction/as a wave in Schrödinger model <em><strong>OR</strong> </em>as particle in Bohr model ✔<br></span></p>
<p><span style="background-color: #ffffff;">reference to «same» energy levels in both models ✔<br></span></p>
<p><span style="background-color: #ffffff;">reference to «relationship between wavefunction and» probability «of finding an electron in a point» in Schrödinger model ✔</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A student makes a parallel-plate capacitor of capacitance 68 nF from aluminium foil and plastic film by inserting one sheet of plastic film between two sheets of aluminium foil.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The aluminium foil and the plastic film are 450 mm wide.</p>
<p style="text-align: left;">The plastic film has a thickness of 55 μm and a permittivity of 2.5 × 10<sup>−11</sup> C<sup>2</sup> N<sup>–1</sup> m<sup>–2</sup>.</p>
</div>
<div class="specification">
<p>The student uses a switch to charge and discharge the capacitor using the circuit shown. The ammeter is ideal.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The emf of the battery is 12 V.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="text-align:left;">Calculate the total length of aluminium foil that the student will require.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="text-align:left;">The plastic film begins to conduct when the electric field strength in it exceeds 1.5 MN C<sup>–1</sup>. Calculate the maximum charge that can be stored on the capacitor.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The resistor <em>R</em> in the circuit has a resistance of 1.2 kΩ. Calculate the time taken for the charge on the capacitor to fall to 50 % of its fully charged value.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The ammeter is replaced by a coil. Explain why there will be an induced emf in the coil while the capacitor is discharging.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest <strong>one</strong> change to the discharge circuit, apart from changes to the coil, that will increase the maximum induced emf in the coil.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>length = <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{d \times C}}{{{\text{width}} \times \varepsilon }}">
<mfrac>
<mrow>
<mi>d</mi>
<mo>×</mo>
<mi>C</mi>
</mrow>
<mrow>
<mrow>
<mtext>width</mtext>
</mrow>
<mo>×</mo>
<mi>ε</mi>
</mrow>
</mfrac>
</math></span></span> ✔</p>
<p>= 0.33 «m» ✔</p>
<p>so 0.66/0.67 «m» «as two lengths required» ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.5 × 10<sup>6</sup> × 55 × 10<sup>-6</sup> = 83 «V» ✔</p>
<p>q «= CV»= 5.6 × 10<sup>-6</sup> «C»✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.5 = {{\text{e}}^{ - \frac{t}{{RC}}}} = {{\text{e}}^{ - \frac{t}{{1200 \times 6.8 \times {{10}^{ - 8}}}}}}">
<mn>0.5</mn>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mfrac>
<mi>t</mi>
<mrow>
<mi>R</mi>
<mi>C</mi>
</mrow>
</mfrac>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mfrac>
<mi>t</mi>
<mrow>
<mn>1200</mn>
<mo>×</mo>
<mn>6.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>8</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
</msup>
</mrow>
</math></span></span></p>
<p><em>t</em> = «−» 1200 × 6.8 × 10<sup>−8</sup> × ln0.5 ✔</p>
<p>5.7 × 10<sup>−5</sup> «s» ✔</p>
<p><em><strong>OR</strong></em></p>
<p>use of <em>t <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> = RC </em>× ln2 ✔</p>
<p>1200 × 6.8 × 10<sup>−8</sup> × 0.693 ✔</p>
<p>5.7 × 10<sup>−5</sup> «s» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>mention of Faraday’s law ✔</p>
<p>indicating that changing current in discharge circuit leads to change in flux in coil/change in magnetic field «and induced emf» ✔</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>decrease/reduce ✔</p>
<p>resistance (R) <em><strong>OR</strong></em> capacitance (C) ✔</p>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many candidates were able to use the proper equation to calculate the length of one piece of aluminum foil for the first two marks, but very few doubled the length for the final mark.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was challenging for many candidates. While some candidates were able to use proper equations for capacitors to determine the charge some of the candidates attempted to use electrostatic equations for the electric field around a point charge to solve this problem.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was also challenging for many candidates, with not an insignificant number leaving it blank. The candidates who did attempt it generally set up a correct equation, but ran into some simple calculation and power of ten errors. Some candidates attempted to solve the equation using basic circuit equations, which did not receive any marks.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This is an explain question, so there was an expectation for a fairly detailed response. Many candidates missed the fact that the discharging capacitor is causing the current in the coil to <span style="text-decoration:underline;">change</span> in time, and that this is what is inducing the emf in the coil. Many simply stated that the current created a magnetic field with not complete explanation of induction.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates who recognized that something about the discharge circuit (not the charging circuit) needed to be changed generally suggested that something had to change with the resistance or capacitance. It should be noted that even though this was the last question on the exam, it was attempted at a higher rate than many of the other questions on the exam.</p>
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>The moon Phobos moves around the planet Mars in a circular orbit.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline the origin of the force that acts on Phobos.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why this force does no work on Phobos.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The orbital period <em>T</em> of a moon orbiting a planet of mass <em>M</em> is given by</p>
<p style="text-align:center;"><span style="background-color:#ffffff;"><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\frac{{{R^3}}}{{{T^2}}} = kM">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>R</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mi>k</mi>
<mi>M</mi>
</math></span></span></p>
<p>where <em>R</em> is the average distance between the centre of the planet and the centre of the moon.</p>
<p>Show that <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = \frac{G}{{4{\pi ^2}}}">
<mi>k</mi>
<mo>=</mo>
<mfrac>
<mi>G</mi>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The following data for the Mars–Phobos system and the Earth–Moon system are available:</p>
<p>Mass of Earth = 5.97 × 10<sup>24</sup> kg</p>
<p>The Earth–Moon distance is 41 times the Mars–Phobos distance.</p>
<p>The orbital period of the Moon is 86 times the orbital period of Phobos.</p>
<p>Calculate, in kg, the mass of Mars.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph shows the variation of the gravitational potential between the Earth and Moon with distance from the centre of the Earth. The distance from the Earth is expressed as a fraction of the total distance between the centre of the Earth and the centre of the Moon.</p>
<p style="text-align:center;"><img src="data:image/png;base64,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"></p>
<p style="text-align:left;">Determine, using the graph, the mass of the Moon.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>gravitational attraction/force/field «of the planet/Mars» ✔</p>
<p><em>Do not accept “gravity”</em>.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the force/field and the velocity/displacement are at 90° to each other <strong><em>OR</em></strong></p>
<p>there is no change in GPE of the moon/Phobos ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATE 1</strong></em></p>
<p>«using fundamental equations»</p>
<p>use of Universal gravitational force/acceleration/orbital velocity equations ✔</p>
<p>equating to centripetal force or acceleration. ✔</p>
<p>rearranges to get <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = \frac{G}{{4{\pi ^2}}}">
<mi>k</mi>
<mo>=</mo>
<mfrac>
<mi>G</mi>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></span> ✔</p>
<p><em><strong>ALTERNATE 2</strong></em></p>
<p>«starting with <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:center;text-decoration:none;text-indent:0px;white-space:normal;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{R^3}}}{{{T^2}}} = kM">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>R</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mi>k</mi>
<mi>M</mi>
</math></span><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">»</span></span></p>
<p>substitution of proper equation for T from orbital motion equations ✔</p>
<p>substitution of proper equation for M <em><strong>OR</strong></em> R from orbital motion equations ✔</p>
<p>rearranges to get <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = \frac{G}{{4{\pi ^2}}}">
<mi>k</mi>
<mo>=</mo>
<mfrac>
<mi>G</mi>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></span> ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{m_{{\text{Mars}}}} = {\left( {\frac{{{R_{{\text{Mars}}}}}}{{{R_{{\text{Earth}}}}}}} \right)^3}{\left( {\frac{{{T_{{\text{Earth}}}}}}{{{T_{Mars}}}}} \right)^2}{m_{{\text{Earth}}}}">
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mrow>
<mtext>Mars</mtext>
</mrow>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mrow>
<mtext>Mars</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mrow>
<mtext>Earth</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mrow>
<mtext>Earth</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>M</mi>
<mi>a</mi>
<mi>r</mi>
<mi>s</mi>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mrow>
<mtext>Earth</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</math></span></span> or other consistent re-arrangement ✔</p>
<p>6.4 × 10<sup>23</sup> «kg» ✔</p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>read off separation at maximum potential 0.9 ✔</p>
<p>equating of gravitational field strength of earth and moon at that location <em><strong>OR <img src="data:image/png;base64,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">✔</strong></em></p>
<p>7.4 × 10<sup>22</sup> «kg» ✔</p>
<p><em>Allow ECF from MP1</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered, although some candidates simply used the vague term “gravity” rather than specifying that it is a gravitational force or a gravitational field. Candidates need to be reminded about using proper physics terms and not more general, “every day” terms on the exam.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Some candidates connected the idea that the gravitational force is perpendicular to the velocity (and hence the displacement) for the mark. It was also allowed to discuss that there is no change in gravitational potential energy, so therefore no work was being done. It was not acceptable to simply state that the net displacement over one full orbit is zero. Unfortunately, some candidates suggested that there is no net force on the moon so there is no work done, or that the moon is so much smaller so no work could be done on it.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was another “show that” derivation. Many candidates attempted to work with universal gravitation equations, either from memory or the data booklet, to perform this derivation. The variety of correct solution paths was quite impressive, and many candidates who attempted this question were able to receive some marks. Candidates should be reminded on “show that” questions that it is never allowed to work backwards from the given answer. Some candidates also made up equations (such as T = 2𝝿r) to force the derivation to work out.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was challenging for candidates. The candidates who started down the correct path of using the given derived value from 5bi often simply forgot that the multiplication factors had to be squared and cubed as well as the variables.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was left blank by many candidates, and very few who attempted it were able to successfully recognize that the gravitational fields of the Earth and Moon balance at 0.9r and then use the proper equation to calculate the mass of the Moon.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A planet is in a circular orbit around a star. The speed of the planet is constant. The following data are given:</p>
<p style="padding-left: 120px;">Mass of planet <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>24</mn></msup><mo> </mo></math>kg<br>Mass of star <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>30</mn></msup><mo> </mo></math>kg<br>Distance from the star to the planet <em>R</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><mo> </mo></math>m.</p>
</div>
<div class="specification">
<p>A spacecraft is to be launched from the surface of the planet to escape from the star system. The radius of the planet is 9.1 × 10<sup>3</sup> km.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why a centripetal force is needed for the planet to be in a circular orbit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of the centripetal force.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the gravitational potential due to the planet and the star at the surface of the planet is about −5 × 10<sup>9 </sup>J kg<sup>−1</sup>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the escape speed of the spacecraft from the planet–star system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«circular motion» involves a changing velocity <strong>✓</strong></p>
<p>«Tangential velocity» is «always» perpendicular to centripetal force/acceleration <strong>✓</strong></p>
<p>there must be a force/acceleration towards centre/star <strong>✓</strong></p>
<p>without a centripetal force the planet will move in a straight line <strong>✓</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>)</mo><mo>(</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>24</mn></msup><mo>)</mo><mo>(</mo><mn>3</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>30</mn></msup><mo>)</mo></mrow><mrow><mo>(</mo><mn>4</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mn>8</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup></math> «N» <strong>✓</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>V</em><sub>planet</sub> = «−»<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>(</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>)</mo><mo>(</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>24</mn></msup><mo>)</mo></mrow><mrow><mn>9</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac><mo>=</mo></math>«−» 5.9 × 10<sup>7 </sup>«J kg<sup>−1</sup>» <strong>✓</strong></p>
<p><em>V</em><sub>star</sub> = «−»<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>(</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>)</mo><mo>(</mo><mn>3</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>30</mn></msup><mo>)</mo></mrow><mrow><mn>4</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup></mrow></mfrac><mo>=</mo></math>«−» 4.9 × 10<sup>9 </sup>«J kg<sup>−1</sup>» <strong>✓</strong></p>
<p><em>V</em><sub>planet</sub> + <em>V</em><sub>star </sub>= «−» 4.9 «09» × 10<sup>9 </sup>«J kg<sup>−1</sup>» <strong>✓</strong></p>
<p><em><br></em><em>Must see substitutions and not just equations.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <em>v</em><sub>esc</sub> = <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn><mi>V</mi></msqrt></math> <strong>✓</strong></p>
<p><em>v = </em>9.91 × 10<sup>4</sup> «m s<sup>−1</sup>» <strong>✓</strong></p>
<p> </p>
<p> </p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Two identical positive point charges X and Y are placed 0.30 m apart on a horizontal line. O is the point midway between X and Y. The charge on X and the charge on Y is +4.0 µC.</p>
</div>
<div class="specification">
<p>A positive charge Z is released from rest 0.010 m from O on the line between X and Y. Z then begins to oscillate about point O.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the electric potential at O.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the axes, the variation of the electric potential <em>V</em> with distance between X and Y.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the direction of the resultant force acting on Z as it oscillates.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce whether the motion of Z is simple harmonic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>k</mi><mi>Q</mi></mrow><mi>r</mi></mfrac></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfenced><mfenced><mrow><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfenced></mrow><mrow><mn>0</mn><mo>.</mo><mn>15</mn></mrow></mfrac></math> <em><strong>OR</strong> </em>240 «kV» for one charge calculated ✓</p>
<p>480 «kV» for both ✓</p>
<p> </p>
<p><em><strong>MP1</strong> can be seen or implied from calculation.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP2</strong> for <strong>MP3</strong>.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>symmetric curve around 0 with potential always positive, “bowl shape up” and curve not touching the horizontal axis. ✓</p>
<p>clear asymptotes at X and Y ✓</p>
<p> </p>
<p><img src="data:image/png;base64,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"></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>force is towards O ✓</p>
<p>always ✓</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>motion is not SHM ✓</p>
<p>«because SHM requires force proportional to r and» this force depends on <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msup><mi>r</mi><mn>2</mn></msup></mfrac></math> ✓</p>
<p><em><strong><br>ALTERNATIVE 2</strong></em></p>
<p>motion is not SHM ✓</p>
<p>energy-distance «graph must be parabolic for SHM and this» graph is not parabolic ✓</p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was generally well approached. Two common errors were either starting with the wrong equation (electric potential energy or Coulomb's law) or subtracting the potentials rather than adding them.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very few candidates drew a graph that was awarded two marks. Many had a generally correct shape, but common errors were drawing the graph touching the x-axis at O and drawing a general parabola with no clear asymptotes.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates were able to identify the direction of the force on the particle at position Z, but a common error was to miss that the question was about the direction as the particle was oscillating. Examiners were looking for a clear understanding that the force was always directed toward the equilibrium position, and not just at the moment shown in the diagram.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was a challenging question for candidates. Most simply assumed that because the charge was oscillating that this meant the motion was simple harmonic. Some did recognize that it was not, and most of those candidates correctly identified that the relationship between force and displacement was an inverse square.</p>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br>