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<h2>HL Paper 1</h2><div class="question">
<p>An astronaut is orbiting Earth in a spaceship. Why does the astronaut experience weightlessness?</p>
<p>A. The astronaut is outside the gravitational field of Earth.</p>
<p>B. The acceleration of the astronaut is the same as the acceleration of the spaceship.</p>
<p>C. The spaceship is travelling at a high speed tangentially to the orbit.</p>
<p>D. The gravitational field is zero at that point.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>B</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A mass <em>m</em> attached to a string of length <em>R</em> moves in a vertical circle with a constant speed. The tension in the string at the top of the circle is <em>T</em>. What is the kinetic energy of the mass at the top of the circle?</p>
<p> </p>
<p>A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{R\left( {T + mg} \right)}}{2}">
<mfrac>
<mrow>
<mi>R</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>T</mi>
<mo>+</mo>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></p>
<p>B. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{R\left( {T - mg} \right)}}{2}">
<mfrac>
<mrow>
<mi>R</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>T</mi>
<mo>−</mo>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></p>
<p>C. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{Rmg}}{2}">
<mfrac>
<mrow>
<mi>R</mi>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></p>
<p>D. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{R\left( {2T + mg} \right)}}{2}">
<mfrac>
<mrow>
<mi>R</mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mi>T</mi>
<mo>+</mo>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>P and Q are two moons of equal densities orbiting a planet. The orbital radius of P is twice the orbital radius of Q. The volume of P is half that of Q. The force exerted by the planet on P is <em>F</em>. What is the force exerted by the planet on Q?</p>
<p>A. <em>F</em></p>
<p>B. 2<em>F</em></p>
<p>C. 4<em>F</em></p>
<p>D. 8<em>F</em></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>Option D was the most frequent (correct) answer, however option C was a significant distractor, perhaps for candidates considering only the change in orbital radius. A relatively high discrimination index was seen with this question.</p>
</div>
<br><hr><br><div class="question">
<p>A small ball of weight W is attached to a string and moves in a vertical circle of radius R.</p>
<p><img src="data:image/png;base64,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"></p>
<p>What is the smallest kinetic energy of the ball at position X for the ball to maintain the circular motion with radius <em>R</em>?</p>
<p>A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{W\,R}}{2}">
<mfrac>
<mrow>
<mi>W</mi>
<mspace width="thinmathspace"></mspace>
<mi>R</mi>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></p>
<p>B. <em>W R</em></p>
<p>C. <em>2 W R</em></p>
<p>D. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{5W\,R}}{2}">
<mfrac>
<mrow>
<mn>5</mn>
<mi>W</mi>
<mspace width="thinmathspace"></mspace>
<mi>R</mi>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Two satellites W and X have the same mass. They have circular orbits around the same planet. W is closer to the surface than X. What quantity is smaller for W than for X?</p>
<p>A. Gravitational force from the planet</p>
<p>B. Angular velocity</p>
<p>C. Orbital speed</p>
<p>D. Orbital period</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>The centre of the Earth is separated from the centre of the Moon by a distance <em>D</em>. Point P lies on a line joining the centre of the Earth and the centre of the Moon, a distance <em>X</em> from the centre of the Earth. The gravitational field strength at P is zero.</p>
<p><img src="data:image/png;base64,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"></p>
<p>What is the ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{mass of the Moon}}}}{{{\text{mass of the Earth}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>mass of the Moon</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>mass of the Earth</mtext>
</mrow>
</mrow>
</mfrac>
</math></span>?</p>
<p>A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{{\left( {D - X} \right)}^2}}}{{{X^2}}}">
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>D</mi>
<mo>−</mo>
<mi>X</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mi>X</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>B. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\left( {D - X} \right)}}{X}">
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>D</mi>
<mo>−</mo>
<mi>X</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mi>X</mi>
</mfrac>
</math></span></p>
<p>C. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{X^2}}}{{{{\left( {D - X} \right)}^2}}}">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>X</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>D</mi>
<mo>−</mo>
<mi>X</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>D. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{X}{{D - X}}">
<mfrac>
<mi>X</mi>
<mrow>
<mi>D</mi>
<mo>−</mo>
<mi>X</mi>
</mrow>
</mfrac>
</math></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>An object of mass <em>m </em>moves in a horizontal circle of radius <em>r </em>with a constant speed <em>v</em>. What is the rate at which work is done by the centripetal force?</p>
<p>A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^3}}}{r}">
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span></p>
<p>B. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^3}}}{{2\pi r}}">
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mi>r</mi>
</mrow>
</mfrac>
</math></span></p>
<p>C. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^3}}}{{4\pi r}}">
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mi>π</mi>
<mi>r</mi>
</mrow>
</mfrac>
</math></span></p>
<p>D. zero</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br>