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Grade 10Mechanics

The two spheres on the right of Fig. are slightly separated and initially at rest; the left sphere is incident with speed v0 Assuming head-on elastic collisions, (a) if M ≤ m, show that there are two collisions and find all final velocities; (b) if M> m, show that there are three collisions and find all final velocities.
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FIJyen48ePh4aG/qAlRuLj41NTU1dWVkBvv6o3XtWaULn6iYkJ0Gjn8Xijo6NpaWkNDQ1dXV2g6W5ubg42HTtz5kxERISOxNgeXLUjEAgGgwECaaRSKXgmpFLp4OCgTCaTSqWPHz8GagcDctvb23Q6fWhoaHNzEzTtcDjcnTt3DAwMDAwMLC0tfXx8QkNDNZ0zbeX58+dRUVGFhYUCgYDD4chksq2trYmJCVWtHugcVOPX19cfPXq0srJCoVAYDEZHR0ddXV1paWlTU1N1dbWDg4OLi8u5c+fOnDljb2+v6lr/s8hkMg8Pj+Li4tnZ2dXVVRDGA0HQzMwMn88HtfelpSWBQCCVSpVK5fDwMIPBSE9Pf/z4MZvNJhAIOByuoaGBQCBERUUZGRmVlJS8++67+fn5OrJO4SEIgvb29oRC4e6fYHt7WyQSqeps+/v74MyfSg9Qb9eBfZr+VEqBQKC+bYNUKt3a2trZ2QFj7AwGQywW9/b2goAtqVQqkUiGhoagb3x7f38/0Hl3dzeTyaTRaKCyRyQSa2pqUChUdHR0WFhYQECAjY1NeXm5eublcrlIJPqOvAuFwp2dHVXed3d3t7a2viPXYrFYPePfXbAA9cqwSCT6/gW7t7cnEAh2dnb+VEoQSaZesN/9y7u7u+oPvVwuFwgEqo+4XK6rq+vw8DCPx2MymaAmL5VKBQLB0tKSQqFYW1ubmZlZW1sbHx+XSqVSqZTL5RYUFExNTY2MjIB5MmVlZUgk0tXV1cHB4datWydOnNDT02trawOXEAqFoIMNIJFIvmXewMBAeno6l8uVy+UzMzMMBoPH48nlclAm4OoKhWJqaqq3t5fP55eXlz99+nRwcJBEIjU1NREIhLq6Ojwef//+/atXr549e/b8+fNGRkZnz5598uTJHy0Q9Rr+ny293d1dVWKlUvlnE6tnViaTbW9vf3d69d5EmUym/pFQKPw+f1iHIAgiEon29vZhYWER3xASEqJ6a21tffv27enpafCFsrIyMzMzDw8PVUqwQ2NwcHB4eHhYWFhwcDASiQRtKvCQHTt2zMvLS/Xj6hdCo9Fnzpyh0+mqh7izs/PLL78MCwtLSUkRi8UdHR09PT0gikYqlfb29oLI2d3d3bm5uY2Njd7eXiD14eHhtbW15uZmNBqdlJRUW1sbFhbm6+ubnJz8wQcfhIaGJiUlqWI8AVNTU76+vs7OzggEAo1GI5HIiIgIFAqFwWAQCAQSibx582ZwcLAq/BaPx3/xxRfA8qioqKioKNUxAoEIDw/Pz89XH8JNSEhwcnKKiIhAIpEIBCIyMhKE9yEQCFB0CARCPbDM19fX09MTiUSGhoaCbS0jIyMj1EChUHw+HyQmEon6+vp37tyJ+P+g0WhQyKdPn1b9lSiVyvb29qCgIPBpcHAwCoUCu2WCb4WHh4eEhKSmpqqMefr0qYGBAchXcHBwfHw8nU4nk8nFxcXAva+vrzOZzLGxMblcDqJrFArFysoKGN9mMBgPHz5cXFwEd7ChoSEzM7OoqMjDw8PBwcHJySk0NDQ+Pt7Z2RmUZGRk5PXr19VX/u/o6AgPD4+MjESj0aCowSja0tISl8tdWVmZnp7m8XggGl+hUMhksrGxMdCG39vbGxkZWV9fHx8fz8jImJ2dHRoaunv3LgaDiYmJAaOAxsbGISEhXV1dtra24EIoFAp0K0RGRiIQiODgYHVBYrHYoKAgVSGj0WhwdivVljkKhVIm3t7dRKFRwcHBUVBS4jygUKiIiAhyEh4cHBQXdvXtXlX5kZMTY2DgiIgI8eKoD8GRGRUWFhoaq+6r+/v7Q0FDVTXdxccnKyvpeao+IiHjrrbc+//xz02/48MMP//d//xccX7p0KTAw8OHDh+ALVVVVp06dOn36tKWlpbm5+fvvv6+np2dpafnee+/p6el9/fXX//7v/+7v7w+qWBAEcTickydPmpiYmJmZgR/88ssvLSwsDA0NTU1NsVjsm2++qf6nGB8ff/jw4TNnzmxvb1OpVAKB0NHRMTg4KJFIdnZ2mEzmzs5OX19fX1/fxsZGRkbG9vZ2X1/fwMDA6uoqkUhsaWkBtzMuLg6Hw/n5+Zmbm7u6up44ccLJycnY2Fg98/39/RYWFjY2Nk5OTjgc7vbt25cuXQoJCUlOTnZwcLh9+/Ynn3wSFBSkSp+amnrixAkjIyMjIyMvLy8vLy+QI29vb3t7+6+//vr27dug3gHw8/M7deqUsbFxQECAs7Ozra3txx9/fPPmzZs3b5qamr733nvOzs7qMdumpqYnT54MCgr65JNP9PX1IyMj7ezsDA0NTUxMTE1NDQ0No6KiNjY2QGISiXT06NELFy6YqmFlZYXD4YyMjL744ouf/vSnqiaxUqmMiYn513/9VxQKZWRkdPToUQwGc+bMmejo6IsXL5qZmZmYmLzzzjvqE4dnZmaOHj1qa2t77ty548ePu7i4tLS0gLGPFy9e9PT0sNnszc3Nvr4+EEvH5XKB2wdqn5ycfP78eVVVFQ6HS01NzcvLA/+haDT61q1bFy5ccHJyys7OTkxM9PT09PDwsLKy+uyzzxISElQGUKnU8+fPm5ubo9HoGzduGBkZ6enp4fF4Op2em5s7MTExPT29vLwMnPzq6urU1BSDweBwOJubm1VVVY2NjXQ6fXl5mc1mp6Sk1NTUdHR0JCUlAfceGRkJmu4rKyupqaloNNrMzEwlY0tLSzs7u5///Ofb29sqexISEn72s59dvHjx4sWLaDQahUJdu3YNCASBQJw7d+7dd99VJRYKhWFhYf/xH//h5OSERCKvXLkSFhZmamp69erVkJAQPT29w4cPnzt3TpWewWC88847hoaG169fDwwMNDU1dXBw8Pf3d3R0BJ2aH3zwgZubmyp9QUHB8ePHL126ZGRkdOnSJTc3t+8zwHwIgqCnT59yuVwOh8P6YxQVFTU1NakespmZmfz8/NbWVoFAMDU1BdIIhcLx8XEWizU1NZWXl9fV1aUuYA6Hs7+/PzIyAhK3tLTs7+/fu3evp6eHxWKlpaWp99P09/cTCISHDx9GRER0dnbKZLKkpKTd3V3wDHV3dw8NDW1sbPT394+Pj4MY7K2trY6ODhqNBl5ra2sTExPBkI+NjY2VlRUCgYiJiQkICPhWD/DGxkZTU1NhYSHoRiIQCMXFxWDcjkAglJaW1tfXqxcim82uqKiorq6urKz8VilRKJSCgoLa2lr1qZ2dnZ0EAqGxsRGk6ezs7O7uVn3l/v37LS0t6vtMVlVVVVVVgWWwQXmyWKzs7Oyuri4Wi5WZmUmlUlXeZmRkJD09Xf0HWSyWTCYbHBxMTU0lk8kpKSmqGpNSqezr6yMQCKmpqSBlX19fS0tLT0/P3bt3h4eHRSJRRkaG+pgFn88nEAhZWVlcLlckEtXU1Ny8ebOzs5NMJpeUlCwsLJSWlq6vrw8NDc3Pz/N4vN7eXi6X++LFC1DbotPpFAqlq6vrwYMHqamp9fX1eDze2dkZg8G4urqGhobGxsYiEIi6urq2traqqqrCwsLCwkLQEQt49uzZgwcPCN9QX1/f0tJSV1fX2dlJp9OfP38+OjpKpVKXl5fHx8d7e3tfvHgxNjbG4XD6+vp4PB4IqsnIyCCTyenp6dHR0bGxsRgMBjjYy5cv+/v7m5ubFxUVYTAYPB5PUKOnpyctLa2np0f9yRwYGEhJSVFPRiQSe3t7VW/V/yslEgmdTicQCCQSicViUanUzMxMFovV1dWVlZUFHgx1X720tEQgEICyCgoKWCxWc3Pz/fv3QQME0NbWpko/Pj5OIBDKysrq6urKy8tZLNb3iQs8uL10hoaGOBxuc3MTPDrt7e1A6pubm9nZ2SBeCkRENjY2Aq+emJgIuuIjIyMtLCxAFdrHx8fFxaW6uhqHw+Xl5Wk6Z9rK8vJydHT03bt3Ozo6RkZGeDweg8EYHx9/8eIFh8PhcDiLi4vApa+trVEolPb29vLy8ry8vAcPHqSkpNy7dy82NjY/Px+DwdjZ2bm5uaFQqISEhI8++ki9AvzdjI+P+/r6EolE8Ejk5uY2Njb29PTQ6fSVlRUul0un04HaVRNyOjo6qFQq8Orl5eVEItHa2trKyio8PNzCwgKJRNra2p4+fXp5efmllt4B4eCqHY1Gh4WFJSYm0ul0KpV69+5dJpMpFAp7e3u3t7c7Ozu5XG57ezsYb6PT6a2trTExMTgcDvgKb29vU1NTX19fU1NTBAJBIpEKCgrUq+UwP4jl5eXExMSKiorc3Fygn+Hh4YmJifz8fA6HU1dXl5ub29PTMzw8/Pz585qamvj4+NzcXBBLA1qepaWlZWVlhoaGhoaGSCSyvLw8Pz8fi8X+oGFRPB4PbndnZyeFQnn+/PnDhw97eno6OjooFIpK7SqRgwDqjIyM6Ohoa2vrnJychIQER0fHwMDApKSkxsbGvr6+EydO6EjA/MFVO5FI/Oqrr9ra2hgMRmdnp0AgYDAYbW1tVCoViJ/FYiUnJ1OpVNB71NXVVVJSYmlpCTqWLl26ZGxsbGFhYW5u7unp2dXVlZOTExERoemcaSs8Hg+FQrm5uS0uLtbX14MaMolE6uvrGxwcpFAoIyMjo6Oj6enpFDVKS0sRCARYx+bSpUuOjo6gNys/P59Op5eWlsbExPT09Hx/M4hEIoFAaG1tzczMrKmpodFoT548GRsby8rKqq+vp9FoLBart7f37t27NTU16enpsbGx5eXlLS0tSUlJMTExV65c8fb2vnHjhomJyczMTG5u7uzsbHp6OjzermGkUulbb72FxWL7+vrweHx5eTmTyUxOTm5oaBgcHBweHi4rK6upqamoqGhqagoNDS0oKAC9qf7+/unp6aGhoT4+Pg4ODmDOU1FRUUxMTdiv9vaazpcVMTEwYGhomJCSUl5c3NzczGIzm5mY6nV5dXV1bW1tVVZWbm5uWllb6DYWFhfHx8f7+/jgcDovFhoaGenh4XL16FYFAVFRUdHR0FBcXl5WVqQJjvg8UCgWBQKBQKNCd0drampKS0tDQAHoQW1paSCRSW1tbdnZ2aWlpeXl5aWkpiLNAo9EkEgmJRJ47d87V1TUkJKS0tHRiYsLd3b2iokKHxtsPJgqFIi0tzcfHB4vFUigUNBodExMDWumgepacnFxXVxcWFubk5DQ3Nwd6U+Pi4tLS0gwNDfX19R0cHPLz80kkEpVKLSsry8nJ0XSetJvV1VU8Hg+GjkpKSkgkUmVlZWpqamVlZXt7O3D4hYWFcXFxWCwWi8W6ubkFBgaWlZXhcLgbN26cOXPGzMzMzc0Nh8OVlZWVlJS4u7uXlJT8UDN8fX2DgoKIRCIaja6srCSRSHFxcaAvsKamJjMzMzIyMj8/v7OzMyEhAYlExsXFgZgLa2trfX39oKAgFxcXBweHtra2lZUVZ2dnHWm0QwdZ7RAESSSS999/38/Pj0KhJCYmYrHYioqKlJSU+vp6HA4HXAf4246Ojga31tXV9cMPPwwODgY9MSQSaWhoqKWlxd/fX310B+bHMTQ09NVXX+Xn53t6eubk5JBIpAcPHsTExNy9e5dCody7dy8gICAvLy8tLY1IJDo7O2Ox2MTExMTExNOnT589ezYnJ6eioqKoqGhubq6yshKNRi8tLf1QG6hU6s2bN0NCQuLj44uLi7OyssrLyzMzMxEIRHFxcW1trZubm7GxcVZWlpub2507dwoLC0Gj/datWxYWFiEhIXg8fmlpaXd3NzExkUgk6kg1HjrgagdTYv7t3/4NDJ9GRUU5ODiUlZVhMJjExMSYmJj8/HxLS0skEhkVFVVUVOTr62tlZQWWHAWxMVQqVS6XczgcDAaj6dy8DqyurhIIhOjo6Pj4eENDw8rKSiKRmJGRQSQSKyoqMjIykpKS7O3tQddJSkoKFovV09MzMTFxd3cPDw/Pycnp7e0dGhqamJgoLy+vrKz8cWZkZGSUlZWVlpbicLjc3NyMjIwHDx4EBQVFRkaC1kRkZGRUVBn8HhEAAAkLSURBVBSo7l29etXY2Njb2/vEiRNeXl5oNJpGo7HZ7Pb29lu3br2CxXAPDgda7RAESSQSJyenc+fOBQcHY7HYoqKiy5cvx8TE1NbWBgUFgb9qEPCnr69vZWXl6+tra2ubnp5eXV2dkZHR29v7+PHjjo4OVXQQzF/I7OzstWvXbG1tSSQSHo8nkUg+Pj5RUVExMTFJSUl2dnbBwcFubm6Ojo6enp56enp6enr29vbBwcHe3t5FRUWzs7MCgaCoqOhbq9/8IObn593d3aOiouLi4q5du5aWlpaZmXn//v2Kioq4uLiSkpKbN2/6+fmBtQnBpa9fv47BYJKSkkBXPI/Hy8/PZzAYujO5HTr4aocgaH9/39nZ+dy5c/7+/gYGBiCMKSAgwMnJydfX9+LFixERESkpKUZGRqGhoTY2NomJibW1tffv32ez2U+ePImNjW1oaNB0Jl4rZmdnzczMfvWrX3l6ejo7OxOJRA8PDxMTEzs7O3d3d0NDQ0tLy7CwME9PTwMDAxMTk4CAADKZ3Nvby2azx8fHS0pKkpKSfkQd/lukp6cbGhq6uLgEBQVlZmZ6enqamJhYWVkFBQVZWlq6ublFRUXZ2dmZmJgcP348LS0NDN8MDg4uLi6yWKzBwUdivwFhdQAvUDkGQWCy+deuWsbHxF198AWKSL1y4EBAQoKenp6+vf/HixY8++ujKlSvR0dHJyckpKSnV1dVgUbTOzs7GxkZNm/8a8vDhQ3t7eyMjI1dX12vXrllbW3t5ebm7u6sL3svLy8PDIyYmBgy8Lyws7Ozs1NfXp6WlLS4u/uU2zM/PJyQkgBUp9PT0vL29Q0NDHR0dg4KCbt26debMGR8fHzQaDXp80tPT29raBgcdiv9fX8/Lyuru7daQfXh3tUDsEQRKJJC0tDYSRgyBne3t7U1NTa2vruLi4mpqa5ORkEokE1lEQCARkMrmmpgb26i+PmZmZq1evnj59OigoyM3N7dNPPwWTC0BMuIuLS0RERGVlZW1t7fDw8NjY2JMnT/r6+tTXDv6rkJOTY2Njc/78eW9vbzc3N1tbWy8vr6KiIlNTUy8vr8TExKampuLiYh6P19PTMzY21tvbS6FQRCLRX9cMrUBr1A5BkEwm6+vr8/b2BoHNoEsmOzubSCQWFxez2Wwqldre3v7w4cOpqanc3FxY6i8boVBYU1Pj6uqKx+Ozs7NxOFxUVFRAQEB7e/vy8nJrayuZTObz+UNDQ0lJSUgk8q8udUBXV1d4eHh4eHh2djYajXZ2dsbj8S0tLaWlpa2trXQ6fW5u7vnz5xkZGb6+vp2dnTro1QHapHbA3t5eYWEhk8kE4zePHz9ub29fWlqam5urra1NT08PCgqCdf4qWVxcJBAIERERYE4Rg8HgcrlMJpPL5QLB5+XlfWuu8csA7A5YV1fX3t4+NTVFo9Gmp6fB8oRFRUV5eXl5eXk/KJLn9UP71A6QyWTT09P5/5+6ujpN26XTPHv27Ft3pL6+/hWHoHO5XBCBr45q/rWOo61qh4GB+aHAaod5fZifn+/t7V1cXPzWypYikWh6enp0dBSsbKUp8zQOrHaY14e8vLz33nsvMTFRfY0QoVBYWlpqYGDg6upKoVB0tosOgtUO8zqxurqqr6+PRCLVG+rNzc3Hjx8/fPgwvJuAdqtdoVDozpQG7QKsIwiOpVLpqwlQLS8vP3ny5I0bN1Sr/c3MzDg5Of3sZz/T09MD243oMtqndrDxI4VCWV1dffbsWUZGxrNnz8RiMVixRLU9GMwrBqzw39raOjo6ClYBLywsfPz48f7+PpvNJpPJr6BjPDs7++LFi7dv3wZq397eDgsLs7S0PHLkSGBgoGodZJ1F+9QuEol8fHyOHDkCFiT85S9/icVi19bWPDw8jh496uLiomkDdRShUJiXl/fuu+86OztvbW2RSKRf//rXkZGRm5ubeDxeX1+/qanpZRuAwWDc3d0jIyOB2svKyvLz8xMSEv7zP/+ztLRUl1vsAO1Tu1wuZzKZb775Jp1OX11dBVOsIAh68uTJp59+eufOHU0bqLuw2WxjY2NwC9hs9oULF27cuAFBUHt7u6+vr/ra2y8DsHJZfn6+v78/l8udnJy8ceMGmOx87NgxNpv9Uq+uFWif2nd2doKCgt5+++3l5eXl5eXf/va3Pj4+crm8r6/v7bfffvDggaYN1FEkEklRUdHhw4cDAgIgCGppaTl27Ji3tzcEQRUVFa9gT67k5GQikVhZWfmb3/ymurra19e3rq5ueXn5iy++OHv27I/bK/41Q/vULhAILCwsPv74Y6lU2tXV9eabb5aUlAiFQiKR+MEHH6hvxgDzKllZWQkJCfn888/7+vr29/ezsrL++7//G+wbl5KSEhIS8rINuHz5MplMZjKZv/nNb3x9fXE43Pz8fHd394cffhgdHa3aY0eX0T61v3jx4ic/+QnYl/POnTunTp2anZ3l8/l+fn5nzpzRtHW6C5vN1tfXd3Z2hiBocXHRz8/PzMwM7PEQHBxcVFT0Uq++uLh48+ZNOp0O1G5mZjYzMwNBEJFIfPvtt1/SbBytQ8vULpfLGQzGW2+99ejRo/X19StXrvj4+EAQtLy8bGlp6eTkpGkDdZfGxsZ33nknOTkZgqDh4WFra2uwM8/o6GhkZOSPXpTqe5Kdne3l5TU+Ps5kMvX09IqKinZ2dra2tq5du3b06NHBwcGXenVtQcvULhaLMzIyzM3NIQh68eKFoaFhVVUVBEFPnz797LPP0Gi0hu3TYZhM5s2bN/v7+yEIGhoaCg8P7+7uhiBodnY2NTX1pc5K3N3dTUtLu3XrFovFmpiYSEpKevTo0c7ODovFun79+vXr18GugbocMwvQMrXL5fKFhQUQFCWRSNhs9urqKgRBIpGosbERHmzXIJubm6r9avl8/vj4ONg7cHd399mzZy91rBvsOTkwMDA3NycWi9fX18Vi8dra2ujo6MA3PHnyRH3jcN1Ey9QOAwPzo4HVDgOjK8Bqh4HRFWC1w8DoCrDaYWB0BVjtMDC6Aqx2GBhdAVY7DIyuAKsdBkZXgNUOA6MrwGqHgdEVYLXDwOgK/wdwkR25xUpO2QAAAABJRU5ErkJggg==

Profile image of Hrishant Goswami
11 Years agoGrade 10
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Profile image of Jitender Pal
11 Years ago
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