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<h2>SL Paper 1</h2><div class="question">
<p>Two pulses are travelling towards each other.</p>
<p><img src="data:image/png;base64,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"></p>
<p>What is a possible pulse shape when the pulses overlap?</p>
<p><img src="data:image/png;base64,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"></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 ion moves in a circle in a uniform magnetic field. Which single change would increase the radius of the circular path?</p>
<p><br>A. Decreasing the speed of the ion</p>
<p>B. Increasing the charge of the ion</p>
<p>C. Increasing the mass of the ion</p>
<p>D. Increasing the strength of the magnetic field</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</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 at the end of a wooden rod rotates in a vertical circle at a constant angular velocity. What is correct about the tension in the rod? </p>
<p>A. It is greatest when the object is at the bottom of the circle.<br>B. It is greatest when the object is halfway up the circle. <br>C. It is greatest when the object is at the top of the circle. <br>D. It is unchanged throughout the motion.</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>A particle of mass <em>m</em> and charge of magnitude <em>q</em> enters a region of uniform magnetic field <em>B</em> that is directed into the page. The particle follows a circular path of radius <em>R</em>. What are the sign of the charge of the particle and the speed of the particle?</p>
<p><img src="data:image/png;base64,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"></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><span style="background-color:#ffffff;">Object P moves vertically with simple harmonic motion (shm). Object Q moves in a vertical circle with a uniform speed. P and Q have the same time period <em>T</em>. When P is at the top of its motion, Q is at the bottom of its motion.</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;">What is the interval between successive times when the acceleration of P is equal and opposite to the acceleration of Q?<br></span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">A.&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{T}{4}">
  <mfrac>
    <mi>T</mi>
    <mn>4</mn>
  </mfrac>
</math></span><br></span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">B.&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{T}{2}">
  <mfrac>
    <mi>T</mi>
    <mn>2</mn>
  </mfrac>
</math></span><br></span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">C.&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3T}{4}">
  <mfrac>
    <mrow>
      <mn>3</mn>
      <mi>T</mi>
    </mrow>
    <mn>4</mn>
  </mfrac>
</math></span></span></span><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><br></span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">D. T<br></span></span></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>The mass at the end of a pendulum is made to move in a horizontal circle of radius <em>r</em> at constant speed. The magnitude of the net force on the mass is <em>F</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>What is the direction of <em>F</em> and the work done by<em> F</em> during half a revolution?</p>
<p> </p>
<p><img 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"></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><span style="background-color: #ffffff;">An object hangs from a light string and moves in a horizontal circle 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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UQTgLM4+ecWbSCeaAIAQmPbwMmTJ2XixInBVkQZIQAgVJWVleazpqbGfCLaCAEAoWpra5Pi4mJpbW2VRCIRbEVUEQIAQkcbiA9CAEDoaAPxQQgAyAraQDwQAnAW8wTyizYQD4QAnEUI5B9tIPoIATiLEMi/U6dOyaRJk6SpqclMJkP0MGMYQNbohLG6ujqpra0NtiBqaAJwFk0gGrq6uqSwsJA2EFE0AQBZpYvJ0QaiiyYAZ9EEooM2EF00AQBZRxuILpoAnEUTiBbaQDTRBOAsTv7Rom2goaFBVq5cKT09PcFW5BshAKcRBNFSXl5uPhsbG80n8o8QAJAzBQUFUlVVJdXV1bSBiCAEAOQUbSBaCAEAOUUbiBZCAEDO0QaigxAAkHO0geggBOAsnSdg5wogerQNFBUVydatW4MtyAcmi8FZTBaLvubmZiktLZXOzk4zjwC5RxMAkDc6c7iiokLq6+uDLcg1mgCcRROIB9pAftEEAOQVbSC/aAJwFk0gPmgD+UMTAJB3tIH8oQnAWTSBeGlpaZGSkhI5efKkeTcxcoMQgLMIgfiprKw0nzU1NeYT2UcIAIiMtrY2KS4ultbWVkkkEsFWZBMhACBSaAO5RQgAiBTaQG4RAgAihzaQO4QAgMihDeQOIQAgkrQNnD17VjZu3BhsQTYQAnCaPibKLh5PXV1dUlhYKE1NTWYyGbKDGcNwlp0ngHjS5SPq6uqktrY22IJsoAnAWUwWiz/aQPbRBABEFm0g+2gCcBZNwA20geyiCQCINNpAdtEE4CyagDtsG9i1a5eUlZUFWxEGmgCAyNM20NDQIGvWrJGenp5gK8JACACIhfLycvPZ2NhoPhEOQgBALBQUFEhVVZVUV1fTBkJECMBZei+A+wFuoQ2EjxAAEBu0gfARAgBihTYQLkIAQKzQBsJFCACIHW0DRUVFsmnTpmALhovJYgBiqbm5WUpLS6Wzs9PMI8Dw0ATgNJaTdpeuI1RRUSH19fXBFgwHTQDOYtkI99EGRo4mACC2aAMjRxOAs2gCfqANjAxNAECs0QZGhiYAZ9EE/NHS0iIlJSXS2toqiUQi2Ip0EAJwFiHgl8rKSvNZU1NjPpEeQgDOIgT80tbWJsXFxbSBDBECcBYh4B/aQOYIATiLEPAPbSBzhAByQt8R++GHHwY/9Tp69Gjw7bLu7u5+t1tnz56VF154IfgpfA888ICMGzcu+OlK06dPlzFjxgQ/Xabbk332s5/lccU8oQ1khhBARnTVxpMnT5rv58+fl2PHjpnv6tVXXw2+9V6R7dixI/jpSrNnz5b58+cHP1020EnWmjJliowePTr4KXypf6dU7e3t8v777wc/XbZv3z55/fXXg5+upI8wJl+Zzp07N/jW9+80adIks0omho82kBlCAEbyyd1eiSef8Gpra81nsuQT+dixY+WGG24w31Xqydq3k1vy/0+VGi7vvPOOnDt3znwfKEBWrVplPq+99lqzYqayjYOwGNzTTz8t7733nmzcuDHYgoEQAp44deqUOREdP37cDLnYk1B/V+yDnXz0xD5x4kTzHeGzvyeVThjbhmFDWFvU5MmTvR+O0uHHwsJCaWpqMpPJMDBCwCH2BKInDzu2nnqStycNe4L/3Oc+J9dccw0n95ixv+szZ87I6dOnLwXFQL9vO8ymn778rjds2CB79uyR7du3B1vQH0IghvRAtwe/jsOnHvj25qaOO3Nl6Cd7I942P91PUm+qJ+8n9mLApTF02kB6CIEI06s9PZB1LDn1ZG/H45Ov8DjR98Ujov2zAZHcGJPvS2h7mDNnjhle0ns72hrjul/RBoZGCESEnvBPnDgh7777rjkok8d+dYxeD0S9StOrem4KpocQyIy9ma37nx1eSt0P9WJj6tSpct1118ViSIk2MDRCIA90x9QD7M033+xzwrdX97aex+VAiypCIBxDXaBoMNx0002RbQy0gcERAjmgB9Fbb70lBw8elNdee+3SkE7yldW0adMYygkZIZA9AwWDHUqaNWuW3HjjjZG4iNGLrrvuukueeuopKSsrC7bCIgSyIPmkr1cfOtaqV/kLFy40B4cO6bh0Ay6qCIHc0ntWeiN6oP0+n6Gwbds2qa6ulv379zOUmoIQCIFeaeiOn7zz6xXRggULzBrnDOvkByGQX0NdDOmfXLVfvd9x2223SVVVlSxatCjYCkUIDJO+xELH9PUKQ4d3onLFg8sIgWjpLxT0YklPynpPYcaMGcG/mR20gf4RAmnSK4nDhw+bHWj16tVmmz5n/aUvfcncyGV4J3oIgWjT4SN99PnAgQNm/oK9kNIr9pkzZ4Z+oqYN9I8QGIQd5tEnC+yNr7Vr15odiRu50UcIxIcea2+//Xafiyx7rIUZCLSBKxECKewVvw7x6Ilfr06WLVsmpaWlZmVCdpx40SBgF48XewweOXJEtmzZYoaNwgoE2sCVCIGAjvHv3Lnz0lVIXV2dOfFne5wSwOCam5v7NISRHpu2Dbz88su0+YuuCj69pBVUrzR0HFKf4tFVNXVmoS7M9dBDDxEAQAToTN/HHnvMHJd6fL7xxhvmeNXjVk/oehxnQhuALp5YX18fbPGbl00g+apfn07Q4R6dqctVARAPeuL/5S9/aWYD2+Gie+65J+0HNLRdaJvo7Oz0/rj3pgnoWKD+4pOv+nXMUR9V0ysDAgCIDz1e9eJNZ+BrO9DjWe/Z6fGtx/lQtF3oBSBtwIMmoCf/xsZGMwaoVww6nrh06VJO+oBjdB6CXtStWLHCPNChN3/Ly8sHvJFMG+jlbAgkn/zVUDsEADckDxWpwY59bQ46s1/vAfrKyRDYvXu3rFmzxnzn5O8v5gn4LfVCcP369VcsJ00bcOyegM5A1GS/8847TbLrY2U63k8AAP7R416Pfz0P2Lk+en7Q84Rl7w08//zzwRb/OBECWv+efvppc2NIl7HVVNdfOid/AHoe0ItCPS/o00N6ntDzhX20tKamxjwpmBwOPon9cJAd+tHnfvWXyRo+sBgOQn/0ZF9ZWWnenmbfMaA/Kz2H+Ca2IaDjfU888YRZ2qGhoYFxf1yBEMBA9PyxdetWuf/++80cg69+9atmJdPW1tY+F5LaFvR9zDpRTd/1rS+BUi69zzuWIaBJ/o1vfIOrfwyKEMBQbCtQEyZMkM985jPmEXIdYdi0adOgQ0S6grAOO+tby+K8dHzsQsDezdf0XrlyJVf/GBAhgHRoK9Anh+zaRMOhy8rr62LjeEEaqxvDus6PBoAO/+haIgQAgDCcPHky+DY8+j4EveGsnxoqcRKbJqATP3QmoE4RT33WF+gPTQBD0VnGemO4o6PDLD0xUldffbXcfffdZigpLhepsQgBbQB6A4cAQKY0CAgB9McGgL7MJkxjx441D6rEJQgiHwL2HgABACAs+tSPnlfCDgDLBkEcFqiL9D0BTWr9Re3atYsAABAavQmcrQBQOrSkS1boPYKoi3QT0CneOgNYbwIDQBj08U9dWiZX9KZzlB8hjWwT0DcG6Yw+fQwUAMKgT+58//vfD37KjajPQo5kE9BflL4M2k7pBoAw2HuMuRblVUoj2QQOHDhgPgkAAGF67rnngm+5pSMbURXJENA1PXx+yQPCoY+H2rkCgI4w/OxnPwt+yi19p3lURW44SH9Ro0ePjvzNFEQfk8WQTNcB0lm9+RLV/TByTcBO3yYAAITp6NGj5vn9fBlsMbp8ilwIHD9+3CzGBABhC2NpCNdELgS6u7tl3LhxwU8AgGyK5I3hs2fPBt+A4eNeADC0yIWAvrknDlOtEQ8EATC4yIWAvrZN6bpBABAW+2rIfJk0aVLwLVoiFwI6q05vDL/yyivBFgAYuXyehOfPnx/ZZaUjeU9gyZIlkZ5hByB+9CT8ta99Lfgpt77+9a8H36InkiGgL3DWxeN0nQ8ACMu3v/3tvMwV0JfRR1UkQ0ATu6qqyqwgGrf3dQKILr3AtPcdc0WHt1lKehj0rTxFRUXmFW0AEAa9wFy3bl1O28CqVauCb9EU6ZfK2LU+eLUkgDDde++9ZqHKbNKXzv/4xz+O/AoIkW0CKpFISENDg1n/O6rrbgCIn2effdacX7LpK1/5SqRvCFuRf9G82rBhg2zZssU8McTCcgDCkM1VRadNm2ZGMKL6IplkkW4Clr5bYNmyZbJo0SJpaWkJtgLA8GkTaG1tDbUR6BCQPuKu7zGOQwCoWISAskFQUlLCo6MAQqEBsHfvXnPiDoM+0bh58+ZYjVjEJgSUBoG9R6BDRAAwUoWFhXLrrbea78OdVXzHHXfIkSNH5Ic//GFkZwYPJFYhoHRISP9n6z2CBx98kDWGAAybnj++973vmfOJnld0eEjH8isrK4N/QwZ8nFRbxJo1a8x/t2fPHpkxY0bwT+IlFjeG+9PV1SWPPPKIvPHGG/LUU0/xUnoAGdEHTRYvXmye49fJqf2N4evN4zNnzsjp06eDLSJTpkwxE85ceUgltiFg2V+kPov7xBNP8PQQgEHpib22ttYsWa/Dyzq64LPYDQel0l+gvpdY30am43la61hqAkAqPS/ovUR9LFTPF3re8D0AVOybQDJ9akjvziutd7r0RNxu0gAIl578Gxsbpbq62vy8fv16ViBI4lQIqORfuK49pON9/MIB/6Se/Lkw7J9zIWDpjeP6+npZsWKFVFRUyHe/+12zgiA7AOC25JP/66+/bp7b13kAHPv9czYELBsGeq9A6dWAvuUnLrP5AKRHj/V9+/b1ufLnWB+a8yFgpV4d1NXVmcdKs72IFIDs0qd9dJkGbf2zZ89m2CdDsX86KF26Q+iTAK+99pqZDKLzC/QpgYULF5odSEMCQDzo8arHrR6/ehzr8azHtR7fepwTAOnzpgn0R2cLbt++3QwV2XagS1LEdeYf4DpdQHLnzp2yevVqc9Wv64lpEDA/aPi8DgFLryoOHz4sL730kplAojuXrlN0++23s3MBeZZ6saZP/OnDHjNnzuSKPwSEQAq9uXTw4EH56U9/Kjt27DA7m9ZLAgHIHR3nf/XVV82KAHoc6ooA+oTPrFmzuNEbMkJgEHoF8sorr1zaEW39ZMgICJe2cbt4m73i1xO/PtbNBVh2EQJpsg1B30uqQ0Zq7dq15sqEqxMgc/aY0j86xq+44s89QmAY7D2E/fv3m7FKvWrRYaMFCxaYlqBPKzBWCfSVfLWvSy8nt2t9WRRj/PlBCIRAxy+PHj1q5iHYlmCr7E033UQowEv2pP/mm2/KgQMHLh0bemN37ty5MmfOHIZ5IoAQCNlAO74NhalTp5qXUFN14Rod3nn77bfNS1b0uX0uiOKBEMgyGwrHjh0zTzvoOuZKa7A+33zDDTfI9OnTzTLYHByIC92vdSlmbcDvvPPOpWFRZa/02a/jgRDIAx0+On78uPm0Y6NK7ytoRSYYECWpJ3ydlZu8z+q9MF1+5cYbb2R4J4YIgQgY6iDTA0yvrFx7rR2iRx+LPnHihHmdojZXvVDhIsVthEBE2WCwjeH999+/NJSkdJz185//vDkgNRxGjx7NYnhIm+5T58+fN8OUeuHx3nvvXRrDVzqkc+2115p9avLkyexbDiMEYkZvvn344YemNbS3t18RDrY56JXamDFjzKfiIPaPnuiV7ivd3d3mU5datmP3yp7s9QVMuq9o0+ShBb8QAo5Ibg56wGuVP3v2bJ+rO70Zreurjx071jQIDQm9ylOERPzYk7z9nesV/blz5/o90SsdUrS/c4ZyYBECHrABcebMGTPWaxtEakgoHWbSl3Dbq0Nl24QOOXE/Ivt0XF6HapRevatMfmd2eJATPdJBCOBSSKjUk45KHm6y7LCTss3CsqGhfA+O5BO6sv9/lb1yV8k3YJPZq3h7gk9ub5zkEQZCAGlLDgvbKpQdb7b6C41k9sSWzN7D6E9yqORa8t8rWerf2Rrs726H46zkv7O9elec3JFLhACyzo5dW3YMO1ly80iVOsadK8ltJ1XycJmVfJVuca8FUUcIAIDHvHnHMADgSoQAAHiMEAAAjxECAOAxQgAAPEYIAIDHCAE4bdSoUcE3YGRc3ZcIAQDwGCEAAB4jBADAY4QAAHiMEAAGoKumwi36Zj70RQgAKZqbm+XWW2+VW265JdgCVxQWFsqCBQvM7xi9WEUUTtPH+tLdxfXE8Oijj8qBAweCLZL2f4t4SH7M84477pAnn3xS5s2bF2wZXCb7UpzQBOA9e+VfWlraJwDgtr1795rfue/NgBCAtzj5Q/keBoQAvMPJH/3xNQwIAXiDkz/S4VsYEAJwHid/DIcvYcDTQXCWPuc/evTo4Cdg5Fw8XRICcJp9JHDs2LFy7tw58z0THB5uGc5KoMn7jov7A8NBcF5nZ6c8/vjj5rse0EA67L6i+47uQ66iCcBpyRN8dMmAzZs3y8MPP5x2M+DwcEs6TcDuG88++6zcf//9Mn78eLPd1clihACc1t+Bm0kYcHi4ZbAQGOjkbxECQAwNduCmEwYcHm7pLwSGOvlbhAAQQ+kcuIOFAYeHW5JDIN2Tv0UIADGUyYGbHAZXX321fPTRR4SAY3R/sL/bdE/+FiEAxNBwDlwbBh988IGsW7cu2AoXfOc735FEIpHRyd8iBIAYcvXARe65ui8xTwAAPEYIAIDHCAEA8BghAAAeIwQAX31ySJ65fpSMGnWvvNj2sciFDjm07Rm5v0i3Xfxz54vSdiH4d+EsQgBO48mgQZw5Ib9+9+LnhOtl8tWt8uLflsmsxatkS4f+wwlSdt8X5XrOEJe4ui/xKwa8dEF+//ZB+ZV+/ev/KIcf/4Ysf/8r8tLBdvnDH/+ftP/rf5dHbpvMCcIDzBMAvPSxtL24TIqXb+39cf5/lb31j8rtE/6k92d4g6AHvNQtp1qPBd//s9Q+8/cEgKcIAcBHn5yQww2Her+XLZK7S3jZjq8IAcBH9qaw3CKVj9wtCc4E3uJXD3jok/Zj0my+zZK/mkYL8BkhAHjnYzn2xmtiikDZHJn+uU+ZrfATIQB45/JN4alfvlmmcBbwGr9+wDcXPpTjLe0Xv0yVeVP+TOgBfiMEAN+cfkv279ZpwTPltunX9G6DtwgBwDOXbgrrchF/ztwA3xECgFc+kTMnftN7U/gL18vEMZwCfMceAHjlnLz9rwfNN24KQ7ELAD7hpjBSsIAcAHiMJgAAHiMEAMBjhAAAeIwQAACPEQIA4DFCAAA8RggAgMcIAQDwGCEAAB4jBADAY4QAAHiMEAAAjxECAOAxQgAAPEYIAIDHCAEA8BghAAAeIwQAwGOEAAB4S+T/A2uRkmkynCXYAAAAAElFTkSuQmCC" width="194" height="205"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The string makes an angle <em>θ</em> with the vertical. The angular speed of the object is <em>ω</em>. What is tan <em>θ</em>?</span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>ω</mi><mn>2</mn></msup><mi>r</mi></mrow><mi>g</mi></mfrac></math></span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>g</mi><mrow><msup><mi>ω</mi><mn>2</mn></msup><mi>r</mi></mrow></mfrac></math></span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>ω</mi><msup><mi>r</mi><mn>2</mn></msup></mrow><mi>g</mi></mfrac></math></span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>g</mi><mrow><mi>ω</mi><msup><mi>r</mi><mn>2</mn></msup></mrow></mfrac></math></span></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><span style="background-color: #ffffff;">An object of mass <em>m</em> makes <em>n</em> revolutions per second around a circle of radius <em>r</em> at a constant speed. What is the kinetic energy of the object?</span></p>
<p><span style="background-color: #ffffff;">A. 0<br></span></p>
<p><span style="background-color: #ffffff;">B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>π</mi><mn>2</mn></msup><mi>m</mi><msup><mi>n</mi><mn>2</mn></msup><msup><mi>r</mi><mn>2</mn></msup></math><br></span></p>
<p><span style="background-color: #ffffff;">C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>π</mi><mn>2</mn></msup><mi>m</mi><msup><mi>n</mi><mn>2</mn></msup><msup><mi>r</mi><mn>2</mn></msup></math><br></span></p>
<p><span style="background-color: #ffffff;">D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msup><mi>π</mi><mn>2</mn></msup><mi>m</mi><msup><mi>n</mi><mn>2</mn></msup><msup><mi>r</mi><mn>2</mn></msup></math><br></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>On Mars, the gravitational field strength is about <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4}">
  <mfrac>
    <mn>1</mn>
    <mn>4</mn>
  </mfrac>
</math></span> of that on Earth. The mass of Earth is approximately ten times that of Mars.</p>
<p>What is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{radius of Earth}}}}{{{\text{radius of Mars}}}}">
  <mfrac>
    <mrow>
      <mrow>
        <mtext>radius of Earth</mtext>
      </mrow>
    </mrow>
    <mrow>
      <mrow>
        <mtext>radius of Mars</mtext>
      </mrow>
    </mrow>
  </mfrac>
</math></span> ?</p>
<p>A. 0.4</p>
<p>B. 0.6 </p>
<p>C. 1.6 </p>
<p>D. 2.5</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</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 of mass <em>m</em> and 2<em>m</em> orbit a planet at the same orbit radius. If <em>F</em> is the force exerted on the satellite of mass <em>m</em> by the planet and a is the centripetal acceleration of this satellite, what is the force and acceleration of the satellite with mass 2<em>m</em>?</p>
<p><img 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"></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>The gravitational field strength at the surface of Earth is<em> g</em>. Another planet has double the&nbsp;radius of Earth and the same density as Earth. What is the gravitational field strength at the&nbsp;surface of this planet?</p>
<p>A. &nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{g}{2}">
  <mfrac>
    <mi>g</mi>
    <mn>2</mn>
  </mfrac>
</math></span></p>
<p>B. &nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{g}{4}">
  <mfrac>
    <mi>g</mi>
    <mn>4</mn>
  </mfrac>
</math></span></p>
<p>C. &nbsp;2<em>g</em></p>
<p>D. &nbsp;4<em>g</em></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</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 constant mass is tied to the end of a rope of length <em>l</em> and made to move in a horizontal circle. The speed of the object is increased until the rope breaks at speed <em>v</em>. The length of the rope is then changed. At what other combination of rope length and speed will the rope break?</p>
<p><img 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"></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>A horizontal disc rotates uniformly at a constant angular velocity about a central axis normal to the plane of the disc.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJkAAACSCAYAAABWm2h5AAARyUlEQVR4Ae2de4hX1RbH10RcSOZehpzBxtKbCqUxVJojkYlDiBQJihCkxNTVCcJEsBz10kN7GOFIchtvxC3pjkT9ESP9IeiIeZUmsBqdrGgyaFDHK4hO42OY8A87l8/xbufMb34zc/Y5+5zfeewFP87vtfdee+3vXmvt19pljuM4YslKIEIJ3BRh3jZrKwFXAhZkFgiRS8CCLHIR2wIsyCwGIpeABVnkIrYFWJBZDEQugZsjLyHhBZw5c0YuXLgg3d3d0t/fLz/++KPL8aFDh+Tbb78dk/va2lqpq6tz/1dTUyPl5eUydepUqayslDvuuGPM9Hn4Q1me5sl+++036erqks7OTjl+/Lh8+OGHsnjxYrnrrrtEAYQnBEhuvfXWMTEASAcGBtyXF6gKpI2NjW7e06ZNkxkzZvjKc8xCU/aHTIPs999/lxMnTkh7e7scOHBAzp4962qdBx980G34SZMmyS233BJZk1F+T0+Pqx2PHDkiTU1NLqiXLl0q9957r9x///2RlZ2kjDMJsq+++koOHz4sL730kjQ0NMi8efMEYKGxSk2//PKLALjdu3e7oK+vr5eHH34404DLDMgwW59//rns2rVLJk6cKKtWrZLZs2cn2jzB88GDB28AbvXq1bJo0aJE8xyok+KTpZna29udxsZGp7a21mlubnZ6enpSWZ0TJ064/IuIWx8+Z4VSq8kwifg4EFoLkxilfxWoBwdIhB+3d+9eefvtt12NzMBh7ty5AXJKTpLUgcwLriw0wGhQ8NZ169atifApR+N3xN/SopIxHw0NDc7ixYsdTGSeqK2tzXUHcAvS6A5I0htrYGDA9VXwuVpbWx0+55GoN/XHZ2tpaUmVHBK9rLR//36ZP3++XL58Wfbt2yfML2XB7xrRrIzyA/Wm/r29ve68G3L57rvvRkmRoJ+SqBXotWrE2NnZmUQWS86TMqFbtmxJvFZLnCajd9JLKyoq3AnVvMyK6+qdhQsXutr94sWLsmzZMmHOLbFU8i7pYQBfA98rb469RwSB3qLV8NV4JpESsQuDuaFNmzZJX1+fO/ttcvcCefPys9idWE0wBmNoNdZI8dlYtlq5cmWifNeSm0vU/Jo1a1zz+O677xrbHgOwWB/E9HZ0dIzRTOn/mY7Jei27S5An9U8MlVK9MuejloNM8qGcYgYPvb29JrNORV4sryHXpMyplWyejFGjaf/LO2GbpbW/IMhW/m0SgFYSkOHY46iacvCZ8lBCZcLS0nUJIN8kaLTYQWYaYPRUlpryahrH6lBJAFqsIMNEmtRgaC16alKH7mMBIK7fSw202ECmnHwqHJbUigAL5knwOcLWJ470pQRaLCAzCTBlHhlBATZL/iWAzHAt4pZb5CCjQmgcKhiW1Ig0G+bxmnOl4x2nTmqc+p0/OFeGCeeS07VzhVNd/bzTeubqsF+DfkE70B5xAi1ykOGQ8wpLSt2bMLdheTGXvs/paHrcEXncaero82Q7CMAVrSeda55fwr412en98hIpyHDMTahnNbmaSf/rytdOU121I3XvOB1XrsPp2plWZ0V1tVPX9HURDTfYtACG+UDdCWfSxTlgigxkVN7EHA3q3UQ+g02TvHdDQHXtpNO6omYI6Ao5BiSvvPKKO1KfM2eO+1y7dq2WCaR9GOnH0XEjAZmpnpIHgF0H0FXnTOvzTrXUOfX1dY6M4YcBKABS+MLX0iFTlmasMiMBGRvpeIWhTJvIYoJRGkxqnNH8MExjIbjU59tuu03bdOIvs1oSJRkHmRoBos2CknLy41DlQXk0ne66ybyunapXtDpnRvD2MXPKRCpweZ/8rkOAFndEN51OGUZBpswkQAtKCqR5Aphz5QdnZz1+WJPzxRdNTp2M7PQDCjSWF1jqPd8HkRtWw8QAbaQ2NwoyfKgwZhIB0auyNU0xkujV9/+fxqhe4ezsuuQ4zkjTGur/jjvPpYDlfT799NODf9J8hz+HjxYFGQMZ6haA6A6nVaXQgvSmqCqqyknW86pz9ovN7oTsED+syLSGl29kBaCqqqpcjcaTz2FcFDo4gA3afl7+Ct8bAxkOpF+AFBOGicFCYeWS/vnG1MXf9ztnh/hg15wrXf926pkrG/bbYK0ABp07iIkczGXwXVhLNJjT0HdGQKYc9WLgGVrc9U8IBq2lnE18griXOorxFet3Y2grx1HTGqOPNk3yTPtFMQgwAjIAo+NHAS7lS2zfvt19b6o3mhR6HvPCGplYBvTKLvRBEoKCQEEjz6xdu9YNJELcVkull8Bjjz0mhCLl1JMpCg0ywjcRXScMUaGZM2fK+vXrhbiulkonAcIhbNy40Y2na4qLUCBTaNfVYufPnzfFv80nAgkobWbqVHookBE9mpinunTu3LkhSdCEBBAmBleWD+EOqXSCP6DNaFfCoxohr4Om8575FJx3vyNKb944l6TFwVQjTO/v9n3pJRCmfQu5DxymYM+ePdLc3BzoOPyECRPcWPo2mIoRPRFJJlgULMyXX34phEEIRYWo8/s5ivkUv2Xb/8UjAaalmJ4KS4F8MsI7EcY8CXHxQ/Uwm3hUCTCg44KNsAOAQCDjhg8iyFjKvgQYAHDXQBgKBDIuZHjkkUfClGvTpkQC3JZCdKQwpA0yZSpNxhALUwGbNloJMDgLazK1Qfb9999bUxltuyYud0zmTz/9FJgvbZAxpOWGM0v5kQBLftyyF5S0biRhXXH8+PHs3Ahank2XQgmEbXctTXb69OnQi+EplHHuWWZilstn1Vq1rkC0QIY/xr2RlvIngQULFty4Olu39log435u7te2lD8JMPH+888/B6q4FsjYOzZ58uRABdlE6ZbAnXfeKd98802gSvh2/MM6f4G4s4kSJYGysrJAgz7fmozt0WF3wCZKYpYZbQkEdf59gwx/zJpK7XbJVAL8soGBAe06+QYZObPzwlJ+JVBTUyPd3d3aAvANMkYWbDa0lF8JlJeXB6q8b5Bx5V1VVVWgQmyibEgAJXPkyBHtyvgGmXbONkHmJBBUyfgGGXNklZWVmROc3wqxpMIr7C5Rv+Vl6X9aB0nyeFwNUL322mvCWVFGVwCNHs21iXm9D123A/iejA06EafLUNL+/+yzz8p9990nq1evvsHajh07hM0CnBPNEwWdkLcgGwUlaDHAVXjIlQtLx40bJ729vbk7jBxE2fj2yUZpi8z+xMRjsRNZmElWP2yQGH9NbzXZKHLCPDz66KPutcte/0uZDUDo/X6UrDLzk9VkhpuSgc6SJUuG3OkNwDZs2CAtLS25AxjuQ21trbaUrbkcQ2TET8PxxwebM2eOu/183rx5gQLNjFFU4n9Gc9fV1Wnz6RtkIDiPc0SYQ5x/zjV8/PHH7jNIJCPtlslQAt8gA8FBVuAzJKuig4As1S+quvgGWVQM2HzTI4GTJ09KRUWFNsO+QUbmFJIMuihHty2SsrJFsu3oxeIsXT4oGyaWycSVu+W/fxT/i/1WTwL9/f0yffp0vUQi4htkZE4hyaAKeeC5V6Wp7pg0rvtIjvYXouiiHP3XO7JVnpcdry+S233XMhm1SyoXhCsIQr7Fz16ioKdVgjA2Zpry2fLctkapO9Qk697vkEH4/yH9Rz+SdY2nZMWORlly+5/GzMr+wZ8EWEpj46Iu+QYZp1XYU5YcuknKH/ibbGuaJYcaX5f3ldns75D31/1TpGmn/GPpX4uqakIhvfDCC8K65HvvvScsE1kaWwKEXmcqR5v8RtEjNixxXhNHQ2726L1+p7fnquVCft944w2noqLCrYu6sGLKlCmR3ClUWHaaP4dpfy3UEMIziTeH3LijqH65Uzfs0vjBpiUIciHAFNC4DdfSyBJAdro3A6vcfJtLVCRzZadOndLWllEnuOn2RfL6jqVyYtd/RJpeleceKD7MZuvwSCZ/+/btUbOZ6vw5rcbKRxDSAhlxMH799dcg5USc5mb5c8VfOE8lc2ZNlZGOO1y9ejViPrKbPYO+YjtS/NRYC2SMLIhPllaaP3/+iJOJrFFaGlkC7Km75557Rv7DKL9ogWzSpEnunTtpHY3RE1988cVhQJsyZYq8/PLLo4gp3z+pNeugIVy19vizWNzQ0OBeUZPWix4A00MPPSSffvqpXLp0yfUzn3zyydztcNXpNoTyZMtTUNICGYVwuRMh1tMKMupA5G4bvds/ZDo6OgRXIyj53hmrCkB1EsM/aBghlY99pkMCJs4zaPlkiAW7TEwMQq1byr4Ejh075rpIYY5DaoMMsaLJMJmWsi+Bw4cPyxNPPBGqotrmktKsyQwl89QkNmEqqWwgTWZNZmpwEopR5kQ5+hfGVAYGGQlXrVoln3zySahK2MTJlsBnn33mhlYPy2Ugc0mhplRp2ArY9NFIgJgfTz31lJFZhEDmkmoxMcvNvVabRdPIpc51//79Q+J/hOEnsCajUDUAYASSt5PUYYSe9LTqhLypWB+BNRmCYgDA9p+9e/cmXW6WPw0JYJ2wUmEdflVkKE1GJsp2W22mRJrup2kthjRCaTIyYGeD1WbpBpaXe9NajLxDazIyUdps3759xlSst+L2fTwSwMdmO5cpX0xxHVqTkRHajPgQdqSpxJrOJyFKiVZkyhdTUjACMjJbvny57Nq1y9VqKnP7TI8E2PDAkbew65TFamwMZKB/48aNQpRsS+mSABPrmzdvFg7TRDEVZQxkiJXdGdDu3bvTJeWcc8vyES7P3LlzI5GEEcffyxmDgLvvvlt6enrceTTvb/Z98iQQx6DNqCZDhPQInEdi31tKtgQwk+vXr5c333zTuLPvrblxkJG5ikTIQMBSciWAD4ZSWLhwYbRMqqPkpp+EMyCsQWdnp+msbX4GJNDe3u62DzEuoiatWBi6zKiKJDF+hm5dsvR/2oMYIMS3iIMiMZdK9zJaIagv/hn231LpJUA7MAvQ1tbmmso4ODI+uizGNM4llLe7iIrJopTfAbA1a9YMuysqap4i1WSKeTRZX1+fcPGVpdJJYNOmTW7h3svI4uAmFpAxi8y62IEDByzQ4mjVImXQwenotEPcpB2mICiDAI2KqlWBuHtTUL6zkA65Hz9+vGR3dMYGMhqLnbQsOVmgxQfdUgOMmsYKMgu0+MBFSUkAGHzE4pMVilZpNOujFUrGzGe1XFRKE+mtSSxTGN4Cve/VkJrv7J3eXskEf59EmZZEkykRqlEnkQ6XLVuWy1volCxMPNk+TRwxAgh/8MEHkewNC8RnHMsKfspoaWlx19JYirKkL4G2tjZ3qYhn0ijStUvdyrKYzqJ6c3OzE8fCrS5/Sfw/ctqyZYsrt7jWInXlUFJzWah6CRHKiSccVpY/UP+WRpYAGw5xM7ibgHOvbNtJJOmiMq7/t7a2uuqfp9VqQ6WOPJR7kUTzOJRbx0mUJvP2QiZs2cJNCAR6K73WkrhhVHHuuSEErR/5hkMTQi9EXRI/01vx1RobG3N70RZ7wKg/ckjb4Cixmszbgeit+ByTJ0+W8ePHuzPZxGzIA1FPZu452c21Q8ghqlNFUckzFSCj8sypsajOEXoo62BT4KKeEPXGhUAOaaPUgEwJlkPExcCWFZ+Nerz11ltuJ1Lgor6mQwcoecbxLOmykokK0uP37NnjmhRmup955hmZNWtWqno8deDWD24R5p5vTuJz80satVbRNk2iox+UJxxinGMOSTBByeekTn/AF/zBp5ffoHVPcrpEzfibElRvb6/DiJSbZmlAgMfnUp+aonzm/RRfPOELfrNMqTeXRdWz50tMUVdXlzsq485GiKB9jNS4v7OysjISf4dyT58+Ld3d3cKNwUTM4bqgBQsWyMyZM1Nn0j0i1X6beZAVSoSlKq645gZiJjRVFCIuRaioqJDp06e7SaZOnSrjxo0rTD7s88DAgAskfgBMkDdPgDxt2jSZMWNGJGAexlACv8gdyIq1AVrnwoULcv78eTl37pz09/e7ACz232LfoRWhCRMmSFVVlTunlRmnvViFNb+zINMUmP27vgRSN0+mX0WbotQSsCArdQvkoHwLshw0cqmraEFW6hbIQfkWZDlo5FJX0YKs1C2Qg/ItyHLQyKWu4v8AwNeKYP4xtyYAAAAASUVORK5CYII="></p>
<p>Point X is a distance 2<em>L</em> from the centre of the disc. Point Y is a distance <em>L</em> from the centre of the disc. Point Y has a linear speed <em>v</em> and a centripetal acceleration <em>a</em>.</p>
<p>What is the linear speed and centripetal acceleration of point X?</p>
<p><img 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"></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>Mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math> is attached to one end of a string. The string is passed through a hollow tube and mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> is attached to the other end. Friction between the tube and string is negligible.</p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> travels at constant speed <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> in a horizontal circle of radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>. What is mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math>?</p>
<p>A.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math></p>
<p>B.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup><mi>r</mi><mi>g</mi></math></p>
<p>C.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><mi>g</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math></p>
<p>D.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mrow><mi>g</mi><mi>r</mi></mrow></mfrac></math></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>Planet X has a gravitational field strength of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mi mathvariant="normal">N</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> at its surface. Planet Y has the same density as X but three times the radius of X. What is the gravitational field strength at the surface of Y?</p>
<p>A.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math></p>
<p>B.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math></p>
<p>C.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>54</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math></p>
<p>D.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>162</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A child stands on a horizontal rotating platform that is moving at constant angular speed. The centripetal force on the child is provided by </p>
<p>A. the gravitational force on the child.</p>
<p>B. the friction on the child’s feet.</p>
<p>C. the tension in the child’s muscles.</p>
<p>D. the normal reaction of the platform on the child.</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>Which is the definition of gravitational field strength at a point?</p>
<p>A. The sum of the gravitational fields created by all masses around the point</p>
<p>B. The gravitational force per unit mass experienced by a small point mass at that point</p>
<p>C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mfrac><mi>M</mi><msup><mi>r</mi><mn>2</mn></msup></mfrac></math>, where <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></em> is the mass of a planet and <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></em> is the distance from the planet to the point</p>
<p>D. The resultant force of gravitational attraction on a mass 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 sphere is suspended from the end of a string and rotates in a horizontal circle. Which freebody diagram, to the correct scale, shows the forces acting on the sphere? </p>
<p style="text-align:center;"><img 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"></p>
<p><img src="data:image/png;base64,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"></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>A satellite is orbiting Earth in a circular path at constant speed. Three statements about the resultant force on the satellite are:</p>
<p style="padding-left:60px;">I.   It is equal to the gravitational force of attraction on the satellite.<br>II.  It is equal to the mass of the satellite multiplied by its acceleration.<br>III. It is equal to the centripetal force on the satellite.</p>
<p>Which combination of statements is correct?</p>
<p>A.  I and II only</p>
<p>B.  I and III only</p>
<p>C.  II and III only</p>
<p>D.  I, II and III</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>This was a good discriminator at HL although many candidates chose option B (D correct). Option B was just the most popular choice at SL. Candidates appear not to realise that although this is circular motion<em> F = ma</em> still applies.</p>
</div>
<br><hr><br><div class="question">
<p style="text-align:left;">Satellite X orbits a planet with orbital radius <em>R</em>. Satellite Y orbits the same planet with orbital radius 2<em>R</em>. Satellites X and Y have the same mass.</p>
<p style="text-align:left;">What is the ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{centripetal acceleration of X}}}}{{{\text{centripetal acceleration of Y}}}}">
  <mfrac>
    <mrow>
      <mrow>
        <mtext>centripetal acceleration of X</mtext>
      </mrow>
    </mrow>
    <mrow>
      <mrow>
        <mtext>centripetal acceleration of Y</mtext>
      </mrow>
    </mrow>
  </mfrac>
</math></span>?</p>
<p style="text-align:left;">A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4}">
  <mfrac>
    <mn>1</mn>
    <mn>4</mn>
  </mfrac>
</math></span></p>
<p style="text-align:left;">B. <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></p>
<p style="text-align:left;">C. 2</p>
<p style="text-align:left;">D. 4</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>A mass at the end of a string is swung in a horizontal circle at increasing speed until the string breaks.</p>
<p>                                                    <img src="images/Schermafbeelding_2018-08-12_om_10.12.50.png" alt="M18/4/PHYSI/SPM/ENG/TZ2/23"></p>
<p>The subsequent path taken by the mass is a</p>
<p>A.     line along a radius of the circle.</p>
<p>B.     horizontal circle.</p>
<p>C.     curve in a horizontal plane.</p>
<p>D.     curve in a vertical plane.</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>A satellite X of mass <em>m</em> orbits the Earth with a period <em>T</em>. What will be the orbital period of satellite Y of mass <em>2m </em>occupying the same orbit as X?</p>
<p>A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{T}{2}">
  <mfrac>
    <mi>T</mi>
    <mn>2</mn>
  </mfrac>
</math></span></p>
<p>B. <em>T</em></p>
<p>C. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2T} ">
  <msqrt>
    <mn>2</mn>
    <mi>T</mi>
  </msqrt>
</math></span></p>
<p>D. 2<em>T</em></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 ball of mass 0.3 kg is attached to a light, inextensible string. It is rotated in a vertical circle. The length of the string is 0.6 m and the speed of rotation of the ball is 4 m s<sup>−1</sup>.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>What is the tension when the string is horizontal?</p>
<p>A.  5 N</p>
<p>B.  8 N</p>
<p>C.  11 N</p>
<p>D.  13 N</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">
<p>This question was well answered by both HL and SL candidates with a high difficulty index for each paper.</p>
</div>
<br><hr><br><div class="question">
<p>An object of mass <em>m </em>at the end of a string of length <em>r </em>moves in a vertical circle at a constant angular speed <em>ω</em>.</p>
<p>What is the tension in the string when the object is at the bottom of the circle?</p>
<p>A. &nbsp; &nbsp;<em> m</em>(<em>ω</em><sup>2</sup><em>r </em>+ <em>g</em>)</p>
<p>B. &nbsp; &nbsp;<em> m</em>(<em>ω</em><sup>2</sup><em>r</em><em>&nbsp;–</em>&nbsp;<em>g</em>)</p>
<p>C. &nbsp; &nbsp;<em> mg</em>(<em>ω</em><sup>2</sup><em>r</em><em>&nbsp;</em>+ 1)</p>
<p>D. &nbsp; &nbsp;<em> mg</em>(<em>ω</em><sup>2</sup><em>r</em><em>&nbsp;–</em>&nbsp;1)</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>A mass attached to a string rotates in a gravitational field with a constant period in a vertical plane.</p>
<p><img src="data:image/png;base64,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"></p>
<p>How do the tension in the string and the kinetic energy of the mass compare at P and Q?</p>
<p><img 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"></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><span style="background-color:#ffffff;">A particle of mass 0.02 kg moves in a horizontal circle of diameter 1 m with an angular velocity of 3<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\pi}">
  <mrow>
    <mi>π</mi>
  </mrow>
</math></span> rad s<sup>-1</sup>.&nbsp;<br></span></p>
<p><span style="background-color:#ffffff;">What is the magnitude and direction of the force responsible for this motion?</span></p>
<p><span style="background-color:#ffffff;"><img 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"></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>A mass at the end of a string is moving in a horizontal circle at constant speed. The string makes an angle <em>θ</em> to the vertical.</p>
<p style="text-align:center;"><img src="data:image/png;base64,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"></p>
<p>What is the magnitude of the acceleration of the mass?</p>
<p><br>A.  <em>g</em></p>
<p>B.  <em>g</em> sin <em>θ</em></p>
<p>C.  <em>g</em> cos <em>θ</em></p>
<p>D.  <em>g</em> tan <em>θ</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">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Three statements about Newton’s law of gravitation are:</p>
<p style="padding-left:30px;">I.   It can be used to predict the motion of a satellite.<br>II.  It explains why gravity exists.<br>III. It is used to derive the expression for gravitational potential energy.</p>
<p>Which combination of statements is correct?</p>
<p>A.  I and II only</p>
<p>B.  I and III only</p>
<p>C.  II and III only</p>
<p>D.  I, II and III</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">
<p>Comments suggested that 'gravitational potential' is more suitable for an HL question. However, candidates should have realised that statement II is incorrect so option B is the only possibility and this proved the most popular answer. The wording will be altered to 'gravitational potential energy' for publication.</p>
</div>
<br><hr><br><div class="question">
<p><span style="background-color:#ffffff;">Which graph shows the relationship between gravitational force<em> F</em> between two point masses and their separation <em>r</em>?</span></p>
<p><span style="background-color:#ffffff;"><img src="data:image/png;base64,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"></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>Newton’s law of gravitation</p>
<p>A.     is equivalent to Newton’s second law of motion.</p>
<p>B.     explains the origin of gravitation.</p>
<p>C.     is used to make predictions.</p>
<p>D.     is not valid in a vacuum.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</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 moves in a circle of constant radius. Values of the centripetal force <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> are measured&nbsp;for different values of angular velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi></math>. A graph is plotted with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi></math> on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis. Which quantity&nbsp;plotted on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis will produce a straight-line graph?</p>
<p>A.&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>F</mi></msqrt></math></p>
<p>B.&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></p>
<p>C.&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>F</mi><mn>2</mn></msup></math></p>
<p>D.&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>F</mi></mfrac></math></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>Two isolated point particles of mass 4M and 9M are separated by a distance 1 m. A point particle of mass M is placed a distance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> from the particle of mass 9M. The net gravitational force on M is zero.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>What is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>?</p>
<p> </p>
<p>A.   <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{{13}}">
  <mfrac>
    <mn>4</mn>
    <mrow>
      <mn>13</mn>
    </mrow>
  </mfrac>
</math></span>m</p>
<p>B.   <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{2}{{5}}">
  <mfrac>
    <mn>2</mn>
    <mrow>
      <mn>5</mn>
    </mrow>
  </mfrac>
</math></span>m</p>
<p>C.   <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{{5}}">
  <mfrac>
    <mn>3</mn>
    <mrow>
      <mn>5</mn>
    </mrow>
  </mfrac>
</math></span>m</p>
<p>D.   <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{9}{{13}}">
  <mfrac>
    <mn>9</mn>
    <mrow>
      <mn>13</mn>
    </mrow>
  </mfrac>
</math></span>m</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p style="text-align:left;">A motorcyclist is cornering on a curved race track.</p>
<p style="text-align:left;">Which combination of changes of banking angle <em>θ</em> and coefficient of friction <em>μ</em> between the tyres and road allows the motorcyclist to travel around the corner at greater speed?</p>
<p style="text-align:center;"><img 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"></p>
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"></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>The gravitational field strength at the surface of a planet of radius <em>R</em> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>. A satellite is moving in a circular orbit a distance <em>R</em> above the surface of the planet. What is the magnitude of the acceleration of the satellite?</p>
<p><br>A.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></p>
<p>B.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>g</mi><mn>4</mn></mfrac></math></p>
<p>C.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>g</mi><mn>2</mn></mfrac></math></p>
<p>D.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></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><span style="background-color: #ffffff;">A satellite travels around the Earth in a circular orbit. What is true about the forces acting in this situation?</span></p>
<p><span style="background-color: #ffffff;">A. The resultant force is the same direction as the satellite’s acceleration.<br></span></p>
<p><span style="background-color: #ffffff;">B. The gravitational force acting on the satellite is negligible.<br></span></p>
<p><span style="background-color: #ffffff;">C. There is no resultant force on the satellite relative to the Earth.<br></span></p>
<p><span style="background-color: #ffffff;">D. The satellite does not exert any force on the Earth.</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>