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<h2>HL Paper 2</h2><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 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BEfwUb+EzMxgJGaF3/65SPjwZvmcWOM/n0/whzfGWebsM83f4tK3j+NQArE0xBOayC5nZaapxxLXp+CL5ysXwfsrxrh4EUeRLmUP/svQnAtjIj82px8dg0Ekttr8LTXy+R1L2Jt41P8/8Epxf8fLJa9y41kWWpff6ZdN7r7RpY124f7FP9/cE3x/weLZe9yI1mW2hT/RanNml2U2AFhRbmU4j+AjLOXjMg/249c73gEktvjMZ3BYvI6Awtr+BDlUor/GvxWo4jIr07Kh5dAILm9BE27nUxed0OWEwIEolxK8Q8AW6k7In+lGO8aS3K7JvPJ65q8jogqyqUU/xFsnLxmRP7JbuRyHRBIbjuAOoHJ5HUCEhZxIcqlFP9FCK6FEZFfm5PProFAcnsNnvZ6mbzuRSzHRwhEufSF+DMoP4lB5kDmQOZA5kDmwDo5UDoYfCH+pQHZd30EKOJsayKQ3CavayKQUR2FQLRHpPgfhfDEdiLyJ3Y5XWtEILltBOpiw5LXixE2sbtRLqX4T0zaUa5F5B9lP+2MQyC5HYd9z5WT157o3st2lEsp/jfIg4j8G4S+fIjJ7ZoUJ69r8joiqiiXUvxHsHHymhH5J7uRy3VAILntAOoEJpPXCUhYxIUol1L8FyG4FkZEfm1OPrsGAsntNXja62XyuhexHB8hEOVSin+E2EL9EfkLhXjbUJLbNalPXtfkdURUUS6l+I9g4+Q1I/JPdmOJ5X777dfPfwvj+++/e40JfO2HMWe15PZ4pD98+OULPt+8+eb4RTYsJq8bAOXjZgSiXErxb4bwugMj8q8b0TjPv/76q5c///zj5dOnTy+IAv99cLWPHz++vH37rb6eck1u+8L8/v3PL2ce5hRN8iok8vosAlEupfg/i+wF5kfkX8D1qV1E6K3480vA2UKR3PZLEQ55I976iSh57cfr3SxHuXQp8WejJRDeuo5qnOx5m1Pj7c1u6Oq/8jUiv3dMYAm2f//91+ZSiCZj8ZUN9wwRRbz5ide3H3/84fPPvvhUGoMw2Lf8UUIxglv/szg+6AN2LS3CvmXunjHv3v30UvLJx8A430Yc5uTDCF61dl7XQiDKpduLv6eZTYkDwUotIr9njAg/Is7aW+Iv4bfjem+82Mc3L+xwTw7IF4kE4q7GM8bYQyjzvC2N73kdwW0pHmLnoATvWy3Cfmve3udwAj5e/Dnc46sOmPDpD3lwS5/leO/6z4yfhddnYsi5cyAQ5VKKv+Mnxd8B8sBXhEA4kngS0sgUYuDfvNiYe/zkKrsSdS/YrFnrU2xeFIjXHhCiWI/ujwr76HVq9vQLj8fNz9nC3o9/9Dv5Rk4h/vDpxZ9c47ltvo8Dgh9jx/e+n4HX3jGm/XMQiHLp0uKvtzQLoe1jEyBwCltvoVztz/qM54RPYwNnPB/10c+mZvvtJqe3CDYYxmB/toZfZzY2TcQRbFh7S/zBGh5s01wvshoD3pYH9cN1qd8+xx/s4psfiy82P5jHWoqJOfajt0f6Wt565cdRV9Yd3cCH2tlqcFPD3s+Hm5IAg3mpX/OZJ17xC/9sY67PN8b7msffUW0GXkfFnusei0CUS7cQf7uhU+SAIUGy4g/kbBZ2Y+CePm3sEnttLhIpbRSyeyx9z1mLyH/O6vZsYbOFCZux8JNVNnjLk/p1RbzhRTzQjw1vR+P9tST+cMyaXvyVA97GDN9HcavY4baEmZ6XriXsS+Pog08r9OQFvGOjpTHWiz8HdFvj2FGuttptWfuZMaN5fcb3nDsXAlEu3UL8faFT/BIJntkTP5uFHc8zvd2JUgRHb/jaNEb85Ct/tq4R+Vvznn0ubLbEX3jqgMV48MXvrbkIA/NLB4ia/yUBioSMfCAvZmyjuBUW1JFqQX1b1xL2tTnil+se4cdmSfypaVvjjFOupvjXmMhnV0Qg2iNuIf4Utm36GZe+mvhLDADPf3Rg0KaxJVJ2/bPvI/J7+7EHGzZ2YSxB57sOBDVfGbdXnEsClG/+NZTLz0pCWh75T28J+3+elu/ICXjeK84l8eewkuJfxjl710OAuim1FP/Km7/Ev/ZWv0fgSgSc0ReR33vtZ7DhMKADVs1PHRSOePNnHdb0v/T4n55r/pz9bBS3xEldsH6tPkp47BX/o9/8S7kC5y35VoqnR99IXnvEkzbHIRDl0tTi798qvCBwevc/OVLYeguUeDPPNnvyr735s0nhg59vbT0jcNZOz/uI/J5rYrsVG8RVnMmnLcGFG+ZYbpjDp6VFAkRuWJvY0gGjxe7ZY0ZxS5zg9IhgRtiXsPN5cMS/+XubigWeZ2kjeZ0Fg/TjGASiXJpa/Pl5ns2YzYJGcdoCZSMgMESGpu8SEok/G5R+lpfYy6a+vxr4/38jtALCPfO1Bj8N44P+j4haBU72R1wj8nv70oqNxgljrvBee6MEfy/SxANfpX4fayRAzGVt5YtyquaLt33m91HcEiMcqNb2xBxh723Aha13PYcT1Z/6oiv++bH6xQI7NLguHfoim2f0j+T1jPhyjfMQiHJpavFnk6D4cZ4P9xJtQYd42+ds/tqQJP4ScNnQxo4NL/7a7BmrtdiEtAZX7KlJuKxNPZvlis8jWoSN8LSYgTuHLHyFPx0EevkdCZDPOfzB31nbKG7BoySswkm1V8Iuwl5zj7xGPtp9Awz9AeFIHx6xNZLXR/zNOfMiEOXS1OL/LJzagHoLybN+9p4fkd973bTfH4Hktj/GI1ZIXkegvuaaUS6l+K/J9xdRReR/MSi/XBKB5PaStG06nbxuQpQDGhGIcinFvxHAKw+LyL9yTOn7/yGQ3K6ZCcnrmryOiCrKpaXFfwTQM64ZkT+jr+nTPgSS2314XWV08noVpub3M8qlFP/5uXvaw4j8pw2ngeEIJLfDKejiQPLaBdZbGo1yKcX/BukQkX+D0JcPMbldk+LkdU1eR0QV5VKK/wg2Tl4zIv9kN3K5Dggktx1AncBk8joBCYu4EOVSiv8iBNfCiMivzcln10Agub0GT3u9TF73IpbjIwSiXErxjxBbqD8if6EQbxtKcrsm9cnrmryOiCrKpRT/EWycvGZE/slu5HIdEEhuO4A6gcnkdQISFnEhyqUvxJ9B+UkMMgcyBzIHMgcyB9bJgdI55gvxLw3IvusjQBFnWxOB5DZ5XROBjOooBKI9IsX/KIQnthORP7HL6VojAsltI1AXG5a8Xoywid2NcinFf2LSjnItIv8o+2lnHALJ7Tjse66cvPZE9162o1xK8b9BHkTk3yD05UNMbtekOHldk9cRUUW5lOI/go2T14zIP9mNXK4DAsltB1AnMJm8TkDCIi5EuZTivwjBtTAi8mtz8tk1EEhur8HTXi+T172I5fgIgSiXUvwjxBbqj8hfKMTbhpLcrkl98romryOiinIpxX8EGyevGZF/shtLLPfbb79+/lsY33//3WtMpb6zgk1u+yD94cMvrzx//fVXL3///VefRSpWk9cKOJM8evfup9ccefPmmyE50gpDlEsp/q0IXnhcRP6FQxrmOmLw559/vHz69OmFov/99/+8lPrOcjC5PR5pxP7t229fDXMI+PHHH45fZMNi8roB0ODH5Aj1TyNH3r//ebBH8fJRLqX4x5gt8yQif5kABwWCQCD+tpX67POj75PboxH9v82cjR1sdbA7fpW6xeS1js/opx8/fvws/vzyl+I/mhG3PoVLEdkPb2x3a2dvJAgiIsi6cMDJeKtRQOKLjZfvvRs+lnzjTU85E/nP2z/zbSv12ec97s/mthQDP3+2vB2zYfJPJcKWeb1b5Bu8yw+u1heekYPsFfZXgN6+Wvsz8Gr9efae2iAmf1j2doW3uCnVp5/z7PdHcoQ1bS7j96wtyqXl3/xJNoI/I4muRn4Pf9kwEUyKnWZ/Ho/Wk/DbAqKweh4AVLg+LzjBI+ryhefkj+IhBm1Q9iBZ6oviPbI/Kuwj16jZAi98aBF/f9iCg55vTJFv7AnkqPIL7uwhD851GLBveDUcjn42mtcj49EeQEw18QdrywM+wKG4ONIn2Xo0R8gd5bxqXzZnu0a5tLz4QwzB+01+NoJ6+hOR32NNcKaAbaNI2OijxjNf4BSX/k0tmvdIv+xK1H1esGatj2eImBX+Ut8jvj0y50xurX/UlcQbzLQR2jH2XnXIVQ3cfK7o2TPXLd/INZ+Pto+DnnKPez/2Gd9a547itdW/PePADzyJqSb+5INwl30OBMzjemR7NkfwVXsWtvyvgEf6+qytKJduK/468QGMP20+C/Zs8yPye/hZ2tC3xB/84cM2/WJjRdY+xyZr+UZBlvo1jucUK3bBxY/FF79ByX/NYZ4+zNe9rnqj1Jo9r6w5ohG3sGPj6yH+2C8JL/iW+oXDlm/M9fnGHHsQIU/Alj7y5ew2itej49Rhm0MUMfnasuuRQ15EVXPRvFE5gl/4qhyxvwzamGa4j3LpluJPknHCVFGToABEIq3YIvJ7xEpRsGGqGPgO1jVBZDPWKVo+iRNxpH5dVXyWM2x4Oxrvr8z3nOstw280CIXflLy9Ud/P5DaKsUX8mcs4y1eJd78GfFqhJy+wA38treQb+ejFH87BstVuy9rPjJmB12f8Z65+xmcvoI6JydeWXYPciN78bd7YOdzfNUc8DtH3KJduJ/7a4L0YkUA+8SIwr9Yfkd8rDgqVNfVhA641Fb1+2mOjgAvmR+IvewgD81uERHO4lsQ/2qBS/C1y/74vCey/R728HgiVE1w5JLaIrfjlukf48aHkG+um+JcYOrYP7IVzVFt2RT+G3KCuyRW4r7U75kgND/sM/ErtduKvE74XFZIHkFo2oxKQM/dF5PfwGRwRbgk5a1DAWz8LC398laBzb+1E/jKOjWZPK4m/Dob+7STFv45sSWD9DL+x8xxcWw/cEoG99VnyjTUlSvJT+8Je+5p/9PXMmj3ad+zxMmVrssR/aV140MGfq34B9C9rpbl3y5ESBqW+KJdS/P8fLYnPLMVfIvHRvoj8R+3V5lHwFL5tj2ys8MEb2lbTQYGrX7c2tyT+jGdNv9FgF/sztjO5jeIvCawfWxJ6ceAPW34uuSCeWWtPjZZ8K+UKnLfkm/et1/cZeH0mNrAkhtLHH7xq6+jQoH9GjMbeMUciLHx/lEu3E3+93ZU2+Na3EA/u7N8j8nv4zWbri3tL/P1bAn5tCS4CwFoUvRpz+LQ0CY+dzzxywPdJeFrsnj3mTG6j2EoC68eSE4yzTRzUxN/nAXWLndYDQMk3bxOfJB7Wv5H3M/B6ZPwS8RrXOoBZbtVX88XzeZccqWFin0W5tLz4S3jshk6ysMmTkDSSBYDsGAve1e8j8nvEBYZsuMKWNRDP2s/+4kgbA1f4qZ32sVfiC25L/T5WCY8fy/dSbtR88bbP/H4mt1FcJYH1Y8kH/6uKsPZj9Z3n5I5v1Gstn+z4km9wCW7YoeFb6dBn7Zx9PwOvR8YMxsSkGi/ZpibJEb088KK2dfC+c46UMCz1Rbm0tPiXfnrSqZKkARQ+sxV+icBn+iLyn7FZmwu2FnsE2TZhbw8IbMSaw4Zd2ySsrUfvI/Gnnw1HucEVf2dtZ3NbwqEksNrsLXZwylhhC84t/zcdpTVb+0q+MReBkR9cWw8Tres+O24GXp+Nwc5XPti6Vp/NEfqUI+wH9pm1d+T9VXOkFYMol5YW/1ZwVh8Xkb963HeIL7ldk+XkdU1eR0QV5VKK/wg2Tl4zIv9kN3K5Dggktx1AncBk8joBCYu4EOVSiv8iBNfCiMivzcln10Agub0GT3u9TF73IpbjIwSiXErxjxBbqD8if6EQbxtKcrsm9cnrmryOiCrKpRT/EWycvGZE/slu5HIdEEhuO4A6gcnkdQISFnEhyqUU/0UIroURkV+bk8+ugUByew2e9nqZvO5FLMdHCES5lOIfIbZQf0T+QiHeNpTkdk3qk9c1eR0RVZRLKf4j2Dh5zYj8k93I5TogkNx2AHUCk8nrBCQs4kKUSyn+ixBcCyMiv6Fm7ksAABSGSURBVDYnn10DgeT2Gjzt9TJ53YtYjo8QiHIpxT9CbKH+iPyFQrxtKMntmtQnr2vyOiKqKJe+EH8G5ScxyBzIHMgcyBzIHFgnB0qHji/EvzQg+66PAEWcbU0EktvkdU0EMqqjEIj2iBT/oxCe2E5E/sQup2uNCCS3jUBdbFjyejHCJnY3yqUU/4lJO8q1iPyj7KedcQgkt+Ow77ly8toT3XvZjnIpxf8GeRCRf4PQlw8xuV2T4uR1TV5HRBXlUor/CDZOXjMi/2Q3crkOCCS3HUCdwGTyOgEJi7gQ5VKK/yIE18KIyK/NyWfXQCC5vQZPe71MXvciluMjBKJcSvGPEFuoPyJ/oRBvG0pyuyb1yeuavI6IKsqlFP8RbJy8ZkT+yW4ssdxvv/36+W9hfP/9d68x/fnnH5/7Pnz45dQ4k9s+cMMj2H799Vcvf//9V59FKlaT1wo4kzyi/uHpzZtvXj5+/DiJV/92I8qlFP9/Y7VcT0T+coGeEBBigNh/+vTpteh///0/L2/ffvvCoYANAKx5dlZLbo9HGrGHUxqHgB9//OH4RTYsJq8bAA1+TN3bw/+IHGmFIMqlU8VfgOGMPoA24mTdCtyz49hE3r//+VkzT82PyH/KaE5+FQhyWo085nCQ4i9ErnlF8Hmbo2502Ds7kqzZsxHftx458u7dT6+TOPSTJ7O2KJdOE3/9jMZVjU0S8cc53qZWbHcWfxVFy+FOP6GRC/r0Pk3Djc1H5Z9yEj8o6tIY8lVvh8zTPwfobUC2el/xcUSDU8sZWLTwzIYpfpnf+6DEeqU80n4kX7SRgyXPEH98IybL81lYj+L1kfjI/Vbxa6mtK+QIh37llXLpEezOmBPl0iniTwHhAElSahTX2ZtmyY8efcR2xzd/hF9vTy2iwNiSyPbgBJsSLr8mXFkhU2Hbw6kEoSRc2PU2e8WA3aiwe65J3PClzY+12LARgBIm8oXxdg5Y9RRWuAQfuya+sHHjq/Yj+LSHPPjTYUB5rBjOuo7g9ZHYwBJfW8S/pbaukiNgpT2EHKYeZm1RLp0i/hTSniKn4EgCnNYHoLWxKOEoUpKOMdinX6SU1lOBY4c5+CWB4sp8bRg8Z03b2CREuJ7jq23Wb+7xA5tqLTY09qgrvp7Z4EVxszYx1xoYMk781cY++4wNH67xkTW52qZnUZ9iUy4yjrxSjHDubVpbR9+fzS3+gyHrWgyEQxQ7+DDHHqK4p8/X0LMYqcaoO/iEE9uoe1/btg+/mEfj3o+1tnrdj+B1TyxwD65gw7VF/Ldq60o5wl5lc4T8mbVFuXSK+AOSFcAtkBAOW3AATQDaWPSdMdqAuBcZeq4NmfW0YbHRMAd7jNfGw5r0iUTm6rDAfObY7/TZNflOEWBHNvmOTcXeYgM7Rzd8OLOJlxIPJT8eEQGwVT5Ym/BX6tcYnsOtcsCPhWP8to21FBNY2g95Jf/pZ9yZ7Wxua7H5+rBjwVn1aftr98wp4QnmpX7ZYp54pR7hzzbmqibVz3j8VyNPwJY+u4/oee/rTLyWYgUT4QqWFrvSePoYE9UWz+HgSjlCHsGT3fOj2Ef2R7l0ivhDui82Egen7IcNOWrYkDBLVNh01STuskESaTxjIEobRmnjJ/HwRfOZgw35HSUmfrE2gs987m2zsW/ZsPOOvMevEU08bW2e4AJOKib8tdyVfIcnio65aszZmqexpRwQh36DIgdYa8Y2iluPhbi2NWnHCEP4wmc+8K2Dsh1r7+FTdUs/9QUXtk7teH/PWImUntm6Vp/8b7Wreb2us/DaEh/cUr+11lJbmSM1BB9/FuXSKeJfKjYbijYEW3gUOcmgxCIAFXGpUH2f5mGTD8kpoeA79pijxjOfwGwc2KGVDivY4MNcvf15odtjQ74cfcXHEU2ceEy8L2zw5IgVAvAW3368/Y4wgD/XVuFnvnJAOUEffvq8oJ8cgMcZ2yhuPRbgU8MfLqkvOwZc4X2riV+urAN3rY3xPo/wQ3UtO8rVPbY1t8d1Fl5bYgNLv3f6eS21lTniUTvme5RLp4g/BV/bPClqHFThsZGrQEksEofvKuJSofo+nTSxzYf5ss+V9ZijpjH6zhWftUmwtn0DseO4bxX/mg1v86jvEflH2Y/siJMt8S/NF572QFAaRx/x1fKrNE85AO9qyhmbFzwjB/bal83e11Hc2rjI6S182AO80IuD6NcCvwaxqobts9o9fmnf0LjSy4hyda992Tz6OgOvrTG1iH9LbWWOtCK+b1yUS6eIf3TqUwhswCpsjbUbAgW5V/yxTdFT/GxOVnS16dhNfkv8txJcPtZ+9t+yITyOvkbkH72Ot6cN9RHxVx5szYVXuONq3yq9L/67csCKP2PIM88hdm3+eFsjv4/iVjGDCzUGnrUmjvwY8PYc+DGay7VlLTu/JP6lXIFzfJmljeZ1Dw6t+9pWbYlnv3bmiEdk3/col04Rf1yFWJwgUdQ4DSLQ9Gvj1gmR8TQ2FYqVMTrBS1TshlPr80mnjX+P+OMXdqwIKCYJlE6ujKXx3cbcYuN14sH/gw8jmjgRPpEPvImJf41hLnhHDQ7Z2JUnjMOGt1ObDy52PmPxxffBue+L7J7dP4pbOAX/VjHmMO/f/FXr9qDv8YNPW3OIdOua2GKs9g3Z9jbph1+7jsaOuo7i9ZF4W8V/q7YyRx5Bf3tOlEuniT8usqFL7HGID9+tCDNOp3CNoTAZp81DorIl/thiDiJixz4i/thiw2ODkF9sLN53CkHP8Zkx9sDTYoO1jmz4M6KJpy3xh1940qEJX8HO4ub953lJkNnYS/1+vnLAj5Uv8plcBL+aQHnbZ34fwa0OseT2nsZ4izf81mwwtiTIcAL/LQ37fixcght2aHBdEqYW+73GjOD10VjgsXZQl92W2socEVrHXaNcOlX8jwun3VKp+NtnrzEyIr93dJH4swngkwQWP+hjA6GfD997tkj86bcHvDN8eSZO/Du7ccAST/4qoYVbjx3Y8lxzwJm+ni2qfwRLfnCV3z192WMbn67SIvEHU3soaKmtzJHjWY9yaWnx1wnfiszx0M5vMSJ/fs/Twy0EktsthK75PHm9Jm8zeh3l0rLiz4mfoHu/Qc5ItvcpIt+Py+/XQyC5vR5nLR4nry0o5ZgWBKJcWlb8W0C5y5iI/LvEv3Kcye2a7Cava/I6Iqool1L8R7Bx8poR+Se7kct1QCC57QDqBCaT1wlIWMSFKJdS/BchuBZGRH5tTj67BgLJ7TV42utl8roXsRwfIRDlUop/hNhC/RH5C4V421CS2zWpT17X5HVEVFEupfiPYOPkNSPyT3Yjl+uAQHLbAdQJTCavE5CwiAtRLqX4L0JwLYyI/NqcfHYNBJLba/C018vkdS9iOT5CIMqlFP8IsYX6I/IXCvG2oSS3a1KfvK7J64ioolz6QvwZlJ/EIHMgcyBzIHMgc2CdHCgdOr4Q/9KA7Ls+AhRxtjURSG6T1zURyKiOQiDaI1L8j0J4YjsR+RO7nK41IpDcNgJ1sWHJ68UIm9jdKJdS/Ccm7SjXIvKPsp92xiGQ3I7DvufKyWtPdO9lO8qlFP8b5EFE/g1CXz7E5HZNipPXNXkdEVWUSyn+I9g4ec2I/JPdyOU6IJDcdgB1ApPJ6wQkLOJClEsp/osQXAsjIr82J59dA4Hk9ho87fUyed2LWI6PEIhyKcU/Qmyh/oj8hUK8bSjJ7ZrUJ69r8joiqiiXUvxHsHHymhH5J7uRy3VAILntAOoEJpPXCUhYxIUol1L8FyG4FkZEfm1OPisj8Ntvv37+Q1jff//d66A///zjc9+HD7+UJ3bqTW77AAuPYPv111+9/P33X30WqVhNXivgTPKI+oenN2++efn48eMkXv3bjSiXUvz/jdVyPRH5ywV6QkCIAWL/6dOn16L//ff/vLx9++0LhwI2ALDm2VktuT0eacQeTmkcAn788YfjF9mwmLxuADT4MXVvD/8jcqQVgiiXphZ/NtN37376/FZFEHzfu7lSyO/f//yKFaRhBxt8uN/ztrZnbCs5vcdF5PdeF/72vjk9MufROMiLEp8UMpjxwf/SGNZkPvmkhmgwfm9+av4j11HcEqvefPABLPa8IYMp83pjxX5R2pi1Pj7wYZwaz3ibo1+HPT0768raV2kcfMGppYEtY4nP1w/zqX+bV5aXFvuPjHk0R+Sb9qxH1j5jTpRL04q/NlIKVxuEEoPCVF8LeCRZSfxb5tox2MDW1VpEfs844EobaKsoPDLn0Ri0wbAZ2SaO5bNEgrd92/huc0H/HKC3ATu25/0Ibqk9uLWiykbYevCx/0yyp4734giX4GP9xAYHNnyFM5r2GuUCV+0xPLM87/Xh0fEjeH3EV71MtYg/Y4Ura5EHPmfAWjwwhnrS3v2If1tzHs0RYlFeaY/YWmvU8yiXphV/kkAnKwuaNp7SMzvO3mNLCaRkfWTTwcaIjcDG8sh9RP4jtlrmUAzCnLUlpLW5j8yp2YueseGzAalgudqmZ7U+CUIph9isvE1r6+j7s7nFfx10fPxs5Fuxq37BGd+9jSPwgR+JButok5Zt9g5/SLN9xKD9RQdSzT3rOoLXPbHBG7iCI9cW8Wec58LmDLz5/QIuWmzv8Z2xz+YINogdf9nryLNZW5RLU4q/3gy4lprvJ0G0mRAoyaJTPfMlRNxb8SeBGa8NS78s0MeHeYyn6YSoZyQPza+tTeP14ST/g89nNooCbIW1sKr5sHcOm4h4s3bBv9SvMTzHH8+9npM74lx9rIV/NGyTF8xXY45ijPzS2KOvZ3Nb8x8catgzF/zBknH4bnH0thkj3O0zarvUrzHMkx9w5QWHuXoZsHPwn8b+os2c+9pamn/0dSZeS7GR78IVLIVdaaz6GK856rM5g03iVi0xBh5rtkflCHuEzZEZ931hHOXSlOK/RbiC4iqBsQcCitUmTKv4M88WOoRaO/7NHz8BVgcNkpaE8Alu/R1xH5Hf2xdxY4t5a83WOYgGvMKBGny1FmFJ/Dn8gRU+2CbeNYcx+sA9uafvNn+sjV73rDtDE2+2Dr1fYEV9gKNqh/tag0+LKTb84as2vyT++ODFX/7LH9YFW+p/T/7WfNnzbBZeW3xuFX8wFv/YJVfAl7pT8zUN91s1PSpH8A2e8NnGoFhmuUa5dHnxLwGsjUWEQI6K3Ra5NnMJCIlpNxpvWyKgfsb7xGRzAmytrbEjrxH5vX0S1ns2z71z4Av+WjYJG6/nnmf4CVb4YJvn3T4bfT+KWx83NeZrwY6hHtjoha1qVGJrx/p78cuVdVrmyAbj/WEcP7QfaJzybo9tze1xnYXXltjAEkxbmgST+Ph4HuxBmufYbeHkjjnSgjdjolxaQvxJDpKIj00uiU6r+GsDACzs+MTkO7ZorMk4ks62SEDsmLPvI/J7+yE8xUPLeo/MIT7x0rIGY0r8IVDYwgfbLO+2f4b7Udza2KmVLfx5bg8H1A2+t2zsrKW6bh0v/1jXi3/Lm7/mj7rOwGtr7NRHi/jDAzyqUW9woT20tHdimzEt7W450oIJY6JcmlL8dfqLfkIkWZQwGgvxJIqeEbBEhw2AZzSJC5tISQAYgw3GY4Ok1ls8fdrkormlBH5deOD/ROT3dklYi4eW9fbOgXf44mrFZWutiD/45tcb27CL/RnbKG6FBbhQE+AZNdUEvpY+/rDl7Yhfrltr+bmM9+JfyhU4bxEwb7/X99G87omLfXELO9Wbry27p3LvhV7zMkf2MPLl2CiXphR/XKdoo82cBFFB+9Mkc0kiApboYIs+msSFpFJisalEjaTWXK7YUsMP72P+7C90/sFaPPzzJL4TP1tz4A4uLHdw4fmIVoq4h1Nrk/mIhe+L7J7dHxV2bz/gB/z5gOXeBp74vjUXPu3Bi/rasyZjtVfIR2+Tfvyx62jsqOsoXh+Jl32xVfy9iNs91d7LD9Wpn6fnXD2fd8kRi0HtPsqlacWfzYWEonC1QfAGToGyQettHOL5rjEQzzwCloCwAZBYNIkL45VY2tixYzcKjVXiYYMxahJ6rjTW8zY0duQ1Ir+3T8JPPLSs1zoHnsSbtUs+lPrtGO4993rOXDiUz+I4+hVK80ZdR3BL7VFj1NWjDZzxXXVbssOYkiDDia3T0lz1lcRfvxb6um3JG9ntfR3B66MxsS9uiT+24Qw+xTlXak24U3PYES/M4Zndc72Pd84Rj0X0PcqlacWfQNhkSBic14fNXcnDGO5JKD3nnoTgu5KoVfxJPmvLJqb80cFCBwLWYJzW1yEjImJEP76NaJGQix8JrPUtmmPHHHFP3oALvtjm86k0xo4ffT+CW2qQdUsfiTLc1rBTDtha7oFlSfxZhzq1/svvHj48YhPfrtIi8QdTfyiwucMzX3/UP5yJG/Zjvej1wuOqOdKKR5RLU4t/a3A5ro5ARH59Vj69AgLJ7RVY2u9j8rofs5xRRiDKpRT/Ml5L9UbkLxXkTYNJbtckPnldk9cRUUW5lOI/go2T14zIP9mNXK4DAsltB1AnMJm8TkDCIi5EuZTivwjBtTAi8mtz8tk1EEhur8HTXi+T172I5fgIgSiXUvwjxBbqj8hfKMTbhpLcrkl98romryOiinIpxX8EGyevGZF/shu5XAcEktsOoE5gMnmdgIRFXIhyKcV/EYJrYUTk1+bks2sgkNxeg6e9XiavexHL8RECUS6l+EeILdQfkb9QiLcNJbldk/rkdU1eR0QV5VKK/wg2Tl4zIv9kN3K5Dggktx1AncBk8joBCYu4EOVSiv8iBNfCiMivzcln10Agub0GT3u9TF73IpbjIwSiXPpC/BmUn8QgcyBzIHMgcyBzYJ0cKB0MPot/6WH2JQKJQCKQCCQCicB6CKT4r8dpRpQIJAKJQCKQCFQRSPGvwpMPE4FEIBFIBBKB9RBI8V+P04woEUgEEoFEIBGoIpDiX4UnHyYCiUAikAgkAushkOK/HqcZUSKQCCQCiUAiUEUgxb8KTz5MBBKBRCARSATWQ+B/AdhOJMx6FPxkAAAAAElFTkSuQmCC"></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>
<br><hr><br><div class="specification">
<p>Rhodium-106 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{\,\,\,45}^{106}{\text{Rh}}">
<msubsup>
<mi></mi>
<mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>45</mn>
</mrow>
<mrow>
<mn>106</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Rh</mtext>
</mrow>
</math></span>) decays into palladium-106 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{\,\,\,46}^{106}{\text{Pd}}">
<msubsup>
<mi></mi>
<mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>46</mn>
</mrow>
<mrow>
<mn>106</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Pd</mtext>
</mrow>
</math></span>) by beta minus (<em>β</em><sup>–</sup>) decay. The diagram shows some of the nuclear energy levels of rhodium-106 and palladium-106. The arrow represents the <em>β</em><sup>–</sup> decay.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-14_om_06.42.36.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/09.d"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Bohr modified the Rutherford model by introducing the condition <em>mvr </em>= <em>n</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{h}{{2\pi }}">
<mfrac>
<mi>h</mi>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
</mfrac>
</math></span>. Outline the reason for this modification.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the speed <em>v </em>of an electron in the hydrogen atom is related to the radius <em>r </em>of the orbit by the expression</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="v = \sqrt {\frac{{k{e^2}}}{{{m_{\text{e}}}r}}} ">
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
<mi>r</mi>
</mrow>
</mfrac>
</msqrt>
</math></span></p>
<p>where <em>k </em>is the Coulomb constant.</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>Using the answer in (b) and (c)(i), deduce that the radius <em>r </em>of the electron’s orbit in the ground state of hydrogen is given by the following expression.</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="r = \frac{{{h^2}}}{{4{\pi ^2}k{m_{\text{e}}}{e^2}}}">
<mi>r</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>h</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>k</mi>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></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>Calculate the electron’s orbital radius in (c)(ii).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what may be deduced about the energy of the electron in the <em>β</em><sup>–</sup> decay.</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>Suggest why the <em>β</em><sup>–</sup> decay is followed by the emission of a gamma ray photon.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the wavelength of the gamma ray photon in (d)(ii).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.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>
<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>
<br><hr><br><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>
<br><hr><br><div class="specification">
<p>There is a proposal to place a satellite in orbit around planet Mars.</p>
</div>
<div class="specification">
<p>The satellite is to have an orbital time <em>T</em> equal to the length of a day on Mars. It can be shown that</p>
<p style="text-align: center;"><em>T</em><sup>2</sup> = <em>kR</em><sup>3</sup></p>
<p>where<em> R</em> is the orbital radius of the satellite and <em>k</em> is a constant.</p>
</div>
<div class="specification">
<p>The ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{distance of Mars from the Sun}}}}{{{\text{distance of Earth from the Sun}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>distance of Mars from the Sun</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>distance of Earth from the Sun</mtext>
</mrow>
</mrow>
</mfrac>
</math></span> = 1.5.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by gravitational field strength at a point.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Newton’s law of gravitation applies to point masses. Suggest why the law can be applied to a satellite orbiting Mars.</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>Mars has a mass of 6.4 × 10<sup>23</sup> kg. Show that, for Mars, <em>k</em> is about 9 × 10<sup>–13 </sup>s<sup>2 </sup>m<sup>–3</sup>.</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 time taken for Mars to revolve on its axis is 8.9 × 10<sup>4</sup> s. Calculate, in m s<sup>–1</sup>, the orbital speed of the satellite.</p>
<p> </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>Show that the intensity of solar radiation at the orbit of Mars is about 600 W m<sup>–2</sup>.</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>Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.</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 atmosphere of Mars is composed mainly of carbon dioxide and has a pressure less than 1 % of that on the Earth. Outline why the mean temperature of Earth is strongly affected by gases in its atmosphere but that of Mars is not.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.iii.</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>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A proton moves along a circular path in a region of a uniform magnetic field. The magnetic field is directed into the plane of the page.</span></p>
<p><span style="background-color: #ffffff;"><img 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"></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The speed of the proton is 2.16 × 10<sup>6</sup> m s<sup>-1</sup> and the magnetic field strength is 0.042 T.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Label with arrows on the diagram the magnetic force <em>F</em> on the proton.</span></p>
<div class="marks">[1]</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;">Label with arrows on the diagram the velocity vector <em>v</em> of the proton.</span></p>
<div class="marks">[1]</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;">For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">For this proton, calculate, in s, the time for one full revolution.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">bii.</div>
</div>
<br><hr><br><div class="specification">
<p>The ball is now displaced through a small distance <em>x </em>from the bottom of the bowl and is then released from rest.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-14_om_06.19.20.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/01.d"></p>
<p>The magnitude of the force on the ball towards the equilibrium position is given by</p>
<p style="text-align: left;"><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\frac{{mgx}}{R}">
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
<mi>x</mi>
</mrow>
<mi>R</mi>
</mfrac>
</math></span></p>
<p>where <em>R </em>is the radius of the bowl.</p>
</div>
<div class="specification">
<p>A small ball of mass <em>m </em>is moving in a horizontal circle on the inside surface of a frictionless hemispherical bowl.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_12.45.38.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a"></p>
<p>The normal reaction force <em>N </em>makes an angle <em>θ</em> to the horizontal.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the direction of the resultant force on the ball.</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>On the diagram, construct an arrow of the correct length to represent the weight of the ball.</p>
<p><img src="data:image/png;base64,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"></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>Show that the magnitude of the net force <em>F </em>on the ball is given by the following equation.</p>
<p> <span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="F = \frac{{mg}}{{\tan \theta }}">
<mi>F</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</math></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The radius of the bowl is 8.0 m and <em>θ</em> = 22°. Determine the speed of the ball.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.</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>Outline why the ball will perform simple harmonic oscillations about the equilibrium position.</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>Show that the period of oscillation of the ball is about 6 s.</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>The amplitude of oscillation is 0.12 m. On the axes, draw a graph to show the variation with time <em>t </em>of the velocity <strong><em>v </em></strong>of the ball during one period.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.</p>
<p> <img src="images/Schermafbeelding_2018-08-12_om_13.41.19.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.d"></p>
<p>The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</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>
<br><hr><br>