Physics-
General
Easy
Question
Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on frictionless horizontal surface. An impulsive force gives a velocity of 14
to the heavier block in the direction of the lighter block. The velocity of centre of mass of the system at that very moment is
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)
- 20
- 10
- 5
The correct answer is: 10![blank m s to the power of negative 1 end exponent](data:image/png;base64,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)
At the time of applying the impulsive force block of 10 kg pushes the spring forward but 4 kg mass is at rest.
Hence,
![v subscript C M end subscript equals fraction numerator m subscript 1 end subscript v subscript 1 end subscript plus m subscript 2 end subscript v subscript 2 end subscript over denominator m subscript 1 end subscript plus m subscript 2 end subscript end fraction equals fraction numerator 10 cross times 14 plus 4 cross times 0 over denominator 10 plus 4 end fraction equals fraction numerator 140 over denominator 14 end fraction equals 10 m s to the power of negative 1 end exponent](data:image/png;base64,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)
Related Questions to study
Maths-
In a Δabc if b+c=3a then
has the value equal to –
In a Δabc if b+c=3a then
has the value equal to –
Maths-General
Maths-
In a
simplifies to
In a
simplifies to
Maths-General
Maths-
In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :
In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :
Maths-General
physics-
A bullet of mass
is fired with a velocity of 50
at an angle
with the horizontal. At the highest point of its trajectory, it collides had on with a bob of massless string of length
m and gets embedded in the bob. After the collision, the string moves to an angle of 120
. What is the angle ![theta ?](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKYAAACkCAYAAAAdQFV8AAAgAElEQVR4nO2993Nc1333/9resMAugAUWvRCNBHsvoqxIohw7iaJkLNuZOIl/SzKT+G/If5HMJB4/mXHm+U7s+dpjayRHtiyFKiwSC0iA6J3odRfbd++9zw/Lc3B2uQBJFBKU8Z7ZIQHcvffce9/ncz79mAzDMNjHPvYYzC96APvYRyHsE3MfexL7xNzHnsQ+MfexJ7FPzH3sSVhf9AD2sXeg6zqGYWA2mzEMg2QySSwWw2QykclkWFlZIRwOY7VaCQQCBAIB7HY7hmFgMpkwmUw7NpZ9ibkPCcMwJDkNwyCdTpNMJjGZTFitVpxOJ7quE4lEiMViZDIZ+b2dJCXsS8x9kCUWgKZp8udEIsHy8jKhUAi73Y7b7SYajWIYhvxdIBDA5XLJ71kslh0b0z4x/8Ch6zq6rmM2mzGb1xfQRCLBwsIC8/PzuN1u7HY78XicaDSKpmnY7Xas1nX67EvMfewIxLKt63qOfphOpzGZTITDYRYXF0kkEgA8fPgQm81GJpMhGAxSXl6O0+mUy7hK6p3APjH/QGEYhlyCzWYzsViMqakppqamqKysxO12EwgEMJvNZDIZotEoRUVFLC4uSn3TarXKc+w09on5BwIhGQXUFIn5+Xl6e3vp7+9naWmJ8+fPc/78eRoaGtA0jWg0Snl5OVarlVu3bpHJZCQhTSYTuq7v+Hj3ifkHAk3TJDHFv4ZhEIvF+PDDD/nss8+oqanhzTff5OjRo3g8HiBr0Hg8HtxuN1arVbqOHA6HJKSw5HdSz9wn5h8IxLIrSKRpGul0muXlZZaWlvjWt77FK6+8Qnl5+WP6omrk1NXVsbKywtraGpqm4fP5gCw5d9IqN+2nvf1hYWVlhWvXrtHT00NraytvvfUWmqZhs9mw2+1PZcTcunWLW7du0dDQwJUrV9B1PYe8O4F9ifkHgnA4zBdffMEXX3xBKBSira2NtrY2HA4H8XgcgGQyid1uf6Lkq6ysxOFwsLi4yPLyMm63+zF303axT8yXHKpuJ3Q+k8kkjRtBlgcPHnDv3j0qKyt58803aWhooKysTEZ1rFYrqVSKp1lAKyoqqKmp4eHDh0xNTdHZ2flU33sW7C/lLznUECIgfYrJZJKZmRlGR0dpbm5G13WWl5fx+/0Eg0FcLpc8XpBb0zQsFssTjRhN0+jr66Orqwuv18u3v/3tHfdl7kvMlxz57ppUKsXKygqDg4PcvXsXm81GfX099fX1NDU15Ug24VgXRHxaPdFkMhEMBonH4zJevu9g30dBCGIsLCzQ1dXF4OAgmUyG48ePU1lZidlsziHwdlw7JpMJn89HW1sbkUiElZUVysvLt30PKvaJ+ZJD13XW1taIRCIUFRURDoeJRqM0NTVx8eJFKioqSKfTOUv9dqGmuS0uLjI3N8drr72GzWbb9rkF9om5hyEIkE8q4YfMZDIsLS0xNDREb28vR44c4fDhw7S1tWGxWKSUNJvNO+r8FuqDpmksLi5y69Ytjh49SkVFRcHxbgX7xNyjEPmQFotFJlxYLBYsFguaphGJRBgZGeE///M/iUajXLx4kUAggMPhwGazSVLspNNbQBg6Ho+HqqoqfD4fw8PDBAIBIGscbXcy7BNzD0N1/wgJKKTR0tIS77//PsFgkG9961s0NzfjdDp33AjZDFarFY/Hg8Vi4datWxw+fJiioqIdkc77xNyjEP5FISnT6TT9/f1MTU1RUVFBbW0t7777Ln6/n5KSEqnfZTIZdF3PkZo7DeGeMplMeDwe6urqGBkZyUns2O6194m5hyGW8+npaW7dusWdO3fw+/3U1tbi9Xrxer24XC4pRVXdbrdICUhjymw243K56OzsJBgM4na7c9xX+0v51wCFDAaTycTQ0BBXr14lmUzS3t5OW1sb9fX1MklX/Y5hGE/lIN8uhEohVAyfzyd9oJqm5RS0bXUs+8TcA1CTdgFWV1eZnp6mpqYGm81GRUUFlZWVtLW1EQgENnTLCP1yt4kpDCphlKXTaQYHB/F6vbS3t2O327d9jX1i7hEIS3tqaoqenh5CoRB/+qd/SnNzMw0NDdhstidaurtNyPzrCAmt6zoTExNomsaBAwdwOBz7OubXBSsrK/T09NDV1cXs7CzHjx/H7/dL6fO8SPc0yA9rOp1O6urq6OnpIZ1Oy2O2M+b9uvIXiFQqRSwWI5lM0tPTw2effYbZbOaHP/wh77zzDm63Wx67k5Gb7UKtPwdwOp20tbWRSCSIRCLSat9OycW+xNxlqK6V/MhNf38/MzMzNDY20tbWRmtrKz6fj6KiIjKZTM7L3W1L+1mQb6AJI8hqtZJIJHLcRlt18O8Tc5ehFoGJMOLi4iLvv/8+H374ISdPnqSyspKSkhLS6TSpVEq+7J1Ovt0p5E8Ss9mM1+vl3Xffpbi4WI57O2PfJ+ZzgFjyUqkUDx484Gc/+xmapvGDH/yA48ePU1FRwfT0NCMjI3i9Xvx+/44n3u4mTCYTNpsNTdMIh8N4vV6cTue+H3Mvw2Qy8fDhQ5aWligqKiIQCPDGG29QXl5OXV0dXq8Xm81GKpVidHQUs9nMwYMH8Xq9L3rozwRd17l//z4Oh4Njx47hdrv3/ZgvEmrURTiWxcuIxWJ0d3dz7do1AC5evMjRo0cpLS2VcW21k0U4HGZpaYmpqSkOHTqUk12kvuS9omuq0HWdWCxGOBwmk8lsWyfeJ+Y2IAijljZA9iUNDw/z5ZdfMjg4iNls5tChQ1RUVMisHMglmGj5Nzc3R1dXFwcOHJCuItUB/zwiO1uBMHRWV1dzmnNtdax7T7N+yaAW+wsdK5VKMT4+Tm9vL16vlytXrnDlyhWqqqpyLFYVKysr8nPv3j0WFhYAChJ/r8IwDFKplOyJtO8uekEQZBFZ5BMTE8zNzXHq1Cnq6ur4zne+Q21tLT6fTyZkFFridF0nHA4TDodJJpPMzc0xODhIVVWVPEZIyr0oLSE70UpKSkilUthstm072PeJuQ2Idinz8/Pcvn2bq1evYjKZ6OjooKWlBbPZTDqdzumoJnyTqislk8lI0jocDtLpNN3d3Zw5cwaHwyFdL3uVlJCdOE1NTZSXl+PxeLbt5ton5gbIJxM8vvwmk0lu3rzJRx99RCgU4vz587zxxhvSlwfIvEg1GpK/LKfTaUKhkDQcotEofX19LC4uUlVVtSd9mfkwm80Eg0GKiopkj6N9ibnD0DSNRCIhE3V1XcfpdD4WxRgbG+Pzzz/H4/Hwl3/5lzKzptBLEb6+/O69Qqo2NDRw8eJFAFpaWmhubsbn88lrqhNlL0pOTdMYHR3l008/5Zvf/CYNDQ3bOt8+MTeA1Wolk8kwOjpKOp2mo6NDNgkQSKfTVFVVUV9fT1tb24akVKFKYMgSzuVycezYMWnNl5WVSVVgL5JwI2QyGWKxmMzJ3E/i2AVYrVZisRgPHjzg7t27LC8vP3aM6sIRDU63ei2v14vD4SCVSuF0OiXJXybspPdgn5gFIBzeq6urjI2NMTQ0xOzs7GPHia1EhItkqwkLgoDJZJJMJvOYZH6ZsFPk3CdmARiGIZMtFhcXmZ2dZXx8XBIHkHqnUPSF1HxaKZff2iWTyZBMJrFYLJSUlMhjCn32GkQAwOPxEAwGdySDfZ+YBSC2E5mfnycajRKNRhkdHWVlZSWHTFarVRLyWSxn1doXutja2hqJRILi4mJKSkpyUuX2MilhPT8zEAhw4sQJiouLty0194lZABaLhVgsxvT0tFTmHz58yMOHD6U0ENJxqy9A7Y6m6zpzc3MkEgmqq6tlG+mXgZSwXmpsMpmoqKjA5XJt28W1T8wNMDc3x/j4OIuLi0QiEaanp+nr69vRRviiy0YymWR2dhZd16mrq8NkMj11r8q9ADFphKEYiUT2Q5K7gVQqRW9vL6urq7J22maz8eDBA+Lx+LYlQr7DfmFhgZmZGVwuFzU1NVJn242t8HYLmqbx4MED7Ha7rPvZDvaJWQBms5nDhw/T0NDAwMCArOkG5JIFuYX/z0pUNTTZ3d1NNBqlpaUFl8slexaJpljpdFrqs6LkQoxDxOALjUEQXHXs55dF7ASETj49Pc0rr7ySU6u0VewTcwM0NTWRTCYJhULE43E6Ozsf8y8WSkV7kpRTpaHVamVwcJD+/n5qa2tpa2vDarXKjsC3b9+mqKiI2tpa2Yp6dXWV4eFhxsbGsNvtnDlzhkAgIAMCY2Nj9PX1kUqlOHDggHTch8NhPv30U1ZXV2ltbaWzs5Pi4uIdeVZi49OZmZmcnNH9kOQOw2w243Q6gXWp4nA4ZB7ldiBcS4ZhsLq6ynvvvYfFYqG9vR2/3y/1ywcPHvCv//qvvPbaa5SWluJyuRgZGeGzzz5jbGwMr9fL1NQUY2NjvPvuu1RVVXHnzh0+//xzpqen0XWdnp4enE4nra2tDAwMsLa2JrOgysrKdoyYYpMqj8eTU1KxT8wdhlgSxXIr9sfZSaRSKT766CNWVlZ47bXXaGhoQNd1xsbG+OKLL+jp6WFsbEwWsCUSCfr7+5mcnKSlpYVDhw4xOTnJjRs3GB8fx+VyMTQ0hGEYvPLKK+i6Tn9/P1988QXV1dXMz8/L5lsmk0nuEbkTsFgslJWV8cd//Mc0NDRgt9vl89qqLv5SEDO/aRTk+gLFzzuF/DJbsfQWGtdGYxO/E24fUUZhGAaRSITbt2/T09PDqVOnOHr0KF6vl1QqxdraGktLSwQCAZqammSbP8MwKCkp4fjx45w4cYJgMEh9fT03btxgdXWVyclJ1tbWOHDgAFeuXCGVSuFyufjkk09YXFyktLSU2dlZ4vE45eXl0om/VeTH+5PJJPX19fj9/h3pybnniZmfwZ2/TUj+MYVqnrd63SdJSzVTWx2jOjZ1qzxN0wiFQvT09HD9+nXa2tq4ePGi3NbEZrMRDAZ58803KSkpYXV1VbqNHA4HR48eRdM03G438Xic0dFRlpaW5LFipzKx705NTQ3RaJTl5WWam5tJJpNyswDRZHU7z0YYfrFYjDt37uB2uwkGg38YxIT1lK/85gGqxFStU/F78bK3ek2VbIUInk9edYwCwrKORCIsLCwwMDBAV1cXtbW1vPXWWzmlularlUAgQCAQIBKJYDKZchKNRURlbW2Nvr4+/ud//ge/309jYyPT09NyPGLsoq9QOp3G5/Px+uuvb+lZFLpvtQnY2toad+7c4ejRo/K5F8o7fRa8FMQUMzCRSEjXibqRu2EYskJP7XK71ZkrHq5w0WzU7kT8TbhwBBHUJgdi6e7v7+fatWtMTk5y5swZ/vzP/1z2kxTZ6/n6mBp/F+dMJpN0d3fz3//93ySTSf7pn/6JYDAoI1TxeFyqH4CM5+80VMEgqjvVZXy7wYE9T0xVUqVSKb744gusViuHDh2iuroaTdNYWFjgN7/5DR988AHV1dW8++67nDhxYsvJBJlMRhJb6IaF9uUWhBFdfIEcv+Hq6irLy8t89NFHXLt2jaqqKv72b/+W48ePy/vaqMmpkPZWqzVHEnZ1dfHBBx9QWVnJ3//931NaWophGBQVFeF2u6WxZLFYiEQiJJPJnP6VOwkxUVZXV3E4HNTV1eXsR/m1tcpVn18ikeC3v/0tv/nNb2hpaaG2tpbq6mqWl5e5evUqd+7c4Y033pA/WywWTp8+vaUXotaIqxnk+RDkVaVjPB5neHiYO3fucOPGDUKhEIcPH+Yf//EfaWtrw+PxSF0vP5+z0BjUz5dffsn7779PJpPh7bffJplMyiYJLpcLt9vN3NwcQ0NDlJSUMDIygmEYeL3eHS3PUMck0v06OjqoqqqSz+NrX/NjGAahUIhf/epX9PT0kEqlKCoqktIwFArR29vLt7/9bY4fP04sFuN3v/sdS0tLrK2t4ff7n/maalRFqAyFliaHw8Hy8jJffvkln332mSzhTSQS+Hw+Tpw4wYEDB2hsbCQQCEjfaL6eDI9LF7PZLBts2e12NE1jZmaGyclJ4vE4P/7xj+XLP3nyJFeuXOHIkSP87//+L//2b/8GQFlZGd/97ncpLS3dUWKazWapLthsNlkKovbF3K6XZE8TU8w8q9VKa2srHR0dXLt2DYfDQSaTIZPJSPdKbW0t5eXlMi9QlMNuhZjqw90sx1LooTabjaKiIkpLSwkGg/h8PsrKymTjfpfLlaPvPs3Ls9vtvPrqq9jtdtxuNxaLhRMnTlBZWfmYh0Jcq7S0FF3Xqa2txTAMqqur6ezszNntYifcauK5iH2GpqamOHLkyI667PY0McVyYbfbOXr0KE6nk/7+flKplJyxiURC6lTiX7/fL9uU7Pb4fD4fZ86c4dixY3i9XkpKSnLKV7e6rFksFg4cOEAikZDnaGhooL6+Pud8qo6qaRrNzc3U1dUB4HK5sNvt8lns1J4/guSJRILJyUkGBwc5cuTIjpxbYE8TE9bbKTudTqmTiW2MIfsC1Z0bICtBgB1JJtgMIou9srKSjo4OOSZhEG2HDCaT6bG8zEKuL0FM8a/dbpfPQ42+7GRhmxAYi4uLTExMyFVjJ7Gr+ZiqLyuVSkmfXCHFXhyf7/8SD1RYviL5QRgMNptN7uAg3DXhcFi6lYCcl6Qq7epY1Ouq/6oWdz7E3zOZzGPRIVUN2A4h7HZ7Tv/1/I+QnmazWR6rGlMWi0V+fyeRTqeZnJxkenqapqamHd+BbdeIKRy7wrIeGxtjZmaGeDye45RWX2g6nZbkzU80FRGURCJBMpmUkkS8iNnZWaLRKPPz89y7d4/p6Wl5bjW0KM6r/pzJZOTEUV1DmqaRTCZJpVIb3mchp7/FYpFG03YJ8aRaIkFO4SEQx1utVmmM7LRKYzabiUajrKysYLPZaGho2LbfMh+7spSLlyvyDdfW1vjNb35DfX09Fy9ezNnEXXVGqw9QEFu8aJvNRjqdRtM07Ha7fAnl5eW0trby4YcfyqL7VCpFTU0NXq83hzTLy8s5UlqQJx6PEwqFcDgcBINBKX3zJetexWak3Q2IVUu05w4EAjt+rR0npiqdBObm5piYmKCurk6mRakOZjXRQfwr/GO6rkv3TSqVoqqqSh6jaZrspjY5OclPfvITkskkf/3Xf83Bgwel3iN6N3788cfcunWL2dlZ0uk0LS0tlJaWMjAwwMDAAJ2dnfzDP/wDTU1NO+b2+DoilUphsVjk/pXine+kE39XJKZwowhyTk1NUVxcTFVVlczQ1nWdaDTK+++/T19fH6WlpTI85/f75RbHHo9HSl+n08lbb72FyZTdwkNERlwuFz/60Y+kte50OnO2j9N1nVQqRVdXF/F4nO9973uYzWZu3rzJ3Nwcr776Kt/85jfp7e3lk08+obq6OsfnKO4pH3tZiu4mwuEwd+/exel0cu7cuR1RWfKx48RUJZ6YQQMDA9jtdoqKiqT/Syynfr9fxliFU1vojZAND66srDA/Py91KVWfE0t+MpnEMLLNBxKJBLquU1xcTE1NjWyYqmkaR44c4ciRI1itViYnJ0kmk5w/fx6bzUYoFJJ1PYLYbrebSCRSsI5FdGJT9eT8DKevA8Q9iX/v3r0rXUTqqraT2DUdU9XTFhYW5IacQjHXdR2Px8OJEyeora2V+mgqlcJsNhMIBLDb7SSTSaanpxkeHiaZTALrcWRd10kkElLJF9cT+2WLSaAaJMKKd7lcOBwOGbITbVri8bh8AcLqBwom1oqk272ug+4EhCH68OFDRkdH8Xq91NXV5TjvdxK75scUg11bWyMWi9HU1CSlkNAl4/E4Q0NDfP755xiGgcfjkUQ7dOgQbreb4uJiKisrZQN9QEpOkeomjKH8EJ/T6cTn80mSqmqEODadTpNIJHC5XDm6rpopJLwF+VAl49ddYorgxfDwMJCtiaqsrMw55qWI/AiLdnFxkUQiQSAQyOk9Lv4uWq4IK9tut0uiQdaZHgwGCQaDZDIZrFYr6XSaxcVFFhYW5DLS2NiYoxfmu3EgS2iRFpbvNlJ9lmpSRn5M+w8ZYtIeOHCA+vp6ueJsp2/TRti1pVwsb/Pz82iaht/vl8QRcLlcnD17llOnTkkpJUhjs9lwOBzSgBJJG7quMzo6yp07d5iampIP5fLlyxw+fDjHmZxPyvLychwOhzymrKwMt9uNx+PBbrdTWloqrX51e2Ph0N8Iqr/160ZgNYk5kUjQ0NCAw+GguLg4x/Oy591FkBtdiUQiBAIBiouLc16uiFQ4HA75HViPFqkJsuLvQme8d+8e9+/fJxgMUlJSQldXF++99x41NTWUlZUVJJHdbufcuXP4fD5KSkowm82cOnUKwzBkr6DDhw9TXl4u96gBHnN9qRDjy89g/7pBpPN1d3dTX19PaWmpTNsTtsFOY1eIqeqAVVVVvPXWW1RWVj52A+osE//PJ5W6pQhkiVJSUsKFCxc4ceIEDocDv9/P+++/n+NLUw0YyBoqhw8fzjm32nxf/FxVVSX9dLDehW2jRGE1pJp/T18HCD38q6++4r333uP73/++dO3tRvKxwK4RU/SO7Ozs3Pb5VKvX4XDw+uuvo+s6KysrdHV1ce/ePerr66UkVNtIbwdCSttstoJJCiaTCbvdLn2q4jtfJ3Lqus7y8jL//u//zp/92Z/JpXy3sSuxcmEtR6NRUqmUbGy6FYhSAbFkiF1exVbKv/zlL+nq6qK4uFhGiET20XYbqQp/qzDICh0n1BHhu/26LeWrq6t89tln1NXV8corr+xIi8Gnwa67i8SSvhUpoiZgiGVDJHO4XC65c+39+/dlh4qWlpac5X8r1xXfUQ2gjaTv19ViV8nn8Xh45513KC8v3/H0to2wqyFJ9YVu5+WpzvNQKMTs7Cwejyen389nn33G/Py87ASxnWuKa8G6D2+jDCOxR8/XYQlXDc1UKkU8HieRSHDq1CnZIx6ejx69axJzKx3QCkGQUiyVmqbR3d1NOp3m3LlzBAIBQqGQdPkICbad5UZ1Makd1wpBzT562YkJSL/y9PQ0vb29eDweXnvtted+b3s6gz2/LEHErj0eD729vfzud7/D6/WytLRETU0NwWBQEkmN7W712uqE2OneRXsVJpOJcDhMX18fQ0NDnD179oVMuD3fUVglp9AtT5w4wbFjx8hkMoyPj2O1Wjl79izl5eU7mkOpdvX4QyFmOp1mYGCAqakp6uvrOXbs2AsZx56WmALqjBVbw1VUVHD58mUSiYR02QCbZps/LdRUt82IqRo+agj0ZYOaOyAadJWWlsqk7hdxXy8FMVUICSpChfl74qj9GbcD1UG/WYa46DyRTqdz0vX2OtTAgBpQsNls0tgJBAI5uQPPEy8dMWFzq3CnSPm041CJ+zL5MIUbTrjDRCmuz+ejurr6sd05njf2vI65j92BMO5EPf7Pf/5zvvzyS6kaqYksLwL7xNwB5MfLXwaIBJTZ2Vn+4z/+g56eHg4ePChzGjYrKXke2JSYhWaMyKHMrxHfrPPu84A6DjUfcytQl2Y1JFrommo+6V7OLlKfiRhjKBTi+vXrDA8P88Ybb8hdM+DJ7XF2G8+sY6oDFWUL6gt5ESE6tZwikUiwsrKC2+2mpKRkW8ZIfj36Rn8XZSR72SJXJ4wqXMrKyvjGN77B+fPnKS4ultLyRYdaNyWmuqWcOli1tibflaC2JXneiEQi3Lt3j6GhIY4cObJtH5waltzo73tVQuZDvKdUKsX4+DgLCwtUVFRw/PhxALmDxV5xeW1KTJHRI4q+xM/io9Zti+ZWVqsVp9P5XIkplp2xsTFu3LjB2NgYwWBwR879onWtnYJ4R4ODg3z11VdkMhleffVVioqKcnJP94rk35SYgmhra2uMjY2xtLQkJabf76e1tRW73c7CwgKTk5MkEgmKioqorKwkGAwWTCTNf9Gqc/dJyJdgqrQyDIPl5WXZv1zUtW8nmVUd12aRn70qNVXpJyI6H3/8MclkkkuXLtHQ0EAqlZK+2L10H09cyg3DoK+vj1/84hcMDQ1JaXn27FkqKytxOp389re/paenR5bV1tfX884771BRUQHkZq3kE1GQXzyUfL+gWmoB2c3mY7GYzPEU5y4qKuL06dMcPnyYn/70p7In+XYg7keUdORDuFuEWrMXJI2AeDbiHUYiEXp7e6msrOTs2bO0trbKQj6hkoly5L2ADYlpGNmG+yZTtpFVbW0tly9f5syZM7Krr8/n4+7du/T19XHhwgXOnTvH2NgYd+/epbu7m9dff10STqSOCaJpmobFYpFNEMbHxzEMg/LycmkZJpNJpqamCIfDVFRUUFVVxfDwML/+9a9lhlE6ncbhcPDDH/6Q119/nUQisSMbhIrJI6I5hbKL1Oyj59GP82khxiMStufm5nC5XLz11lty9zL1+ezFaNWGxBR12SaTSW4gn0gkGBoawuFwUFFRgclkor+/n8rKStrb22Wd8cLCAqOjoySTyZz6n9HRUT799FOGhoYAZPVkaWkpw8PDhEIhjh8/zje/+U0sFgsffPABt2/fBrKZ1FeuXOHNN9/kBz/4AbFYLMf4EBsqqSHLncKTlri9tATC+qozMzPD+++/TygU4q/+6q+orq7OeS57kZACmy7lwg20urpKX18fo6OjOJ1OotEoJ0+e5Pvf/z6hUCin2lHc+OrqqpyxInE4nU6zvLxMcXExly9fJhwO86tf/Qqfz8d3v/tdJiYmGBsbY2xsjKKiIlZWVnj11Vc5e/Ys3d3dxONxzGYzFRUVkuzqMioavNbX11NWVrZj5HySJNwrklJgZWWF27dv8/HHH6NpGu+88w6lpaVy2c5kMlJg7FU80So3mUw0NzfjcrlkHXZvby83b97k2LFjOb2I1HobtQWz0BHj8bjMPD916hRTU1N4vV4aGhro7OzE4/GwsLBAJpPB5XJhtVq5efMm4XCYhoYGmpubKSsry0mWEHqSWjh24sQJPB7PlssA8t1fov0hIP2laoXki5KY4vQudMYAACAASURBVP0IXdJkyja4nZiYoKenh8bGRk6fPk1LS4vMvhLPaK9Npnw80fjRdZ3m5mYaGxvx+Xw4nU6Ki4vp6+tjcnISt9vN2toaqVRKxldF6pmmaTnp+BaLBZ/PR0VFBUVFRdhsNux2Oz6fT7ZoFqSuqKjgwoULWCwWJiYmmJmZoa2tTe4aK4iZb9FbrVZqa2u3vZyLPkmCkEJvi8fjOc3+xb0+j7S3/GtkMhlsNpvcVmVtbY2Kigp8Ph9nz56lqqoqp6nqi3aaPws2JaZwFY2MjOByuSgqKpJRDtEky+l0MjQ0RDgcJpPJEAqFWFpawuv1yopGIT1F5aLqglFrtoV0EvUmbrebK1eusLKywr1797hz5w61tbUEAoEcnVKFSEXbLhYWFpiZmWFkZIT5+XmZpFxdXY3D4cixxlXrfzfIqdbUw7q3JJPJMD8/z/379+nt7ZXbr7S3t9PQ0CC//7KQUcWmxBTumtu3b5NMJgmHw5SXl8uN2pubm8lkMty4cYP+/n4AxsfHWVxclM0IYP3BqK4e8bCTyaRUBZLJpCTq7OwsX331FbW1tbS3t9PS0sLc3NxzK3MIh8Ncv36d3t5ewuEwAwMDhMNhvve97+X4R5+HFFJbgqukXFxc5Pe//z2Dg4N4vV6ampqorq7e1UYEzwub3kE6naaoqIiOjg6++OILPv74Y9xuN6FQiPb2dmpqatB1nYMHD3Lv3j3u3r0LZDuBHTx4EFiXIEIPElt8CL9ZeXk5Xq8XQC7rJSUlUln/8MMP6erqIhaL0d7eTnt7uzx+t2AY2b6dmqaxsrJCKBTC6XTKrh8iKVgcu5s6phAOatWi8JjMzc0xOjrKxYsXOXXq1IbtcV5GPHFqmc1m/uiP/oiWlhaGh4eJRqNUVVVx5MgRuV3JW2+9RV1dHSMjIwQCAU6ePElJSUlOb0rDMGhra6OhoUFuWxwMBvmbv/kbGT5saGiguLhYErSmpobh4WFmZmZobGyU2S+7LaEymQx+v5+mpiYGBweJx+NUVVVx6NAhPB6PDN0JqKUX6lKuGkdCsm40dpXgaiIFZFeVpaUlhoaGuH//PpqmceXKFY4dO0ZHRwcej0fq98I4e9kJuikxxVLsdDppbW2ltbW14HElJSWcP3+ec+fOPVYHI2CxWOT+O4Ds6NbR0SH9nWLnXPE9v9/P6dOn5Xeel64ktqJrbm7G5/MxMDAgt2xWm0gJK1hIs/zN6TVNkzXnQt8WBqWAsKaFG8dkMsn2fiK48fvf/56bN28SjUZpbGzklVdeobW1VRqPAqpB+LLjiX7Mp4E4rpAhshGE20KVKvF4XHb9fZEQBprP5yMQCMgdzwKBQE5M2TAM2QxWzctUz5Pf8EEQ0G63S0tfeBDETsJjY2M8ePCApqYmTp8+TTAYlCHekpIS2Sspvy/l14GQAi9USxYvIpVKyfYje2EJElLM7/dTV1dHQ0MDVVVV+Hw+YD1cq2ka7e3tcj/LRCJBTU1Nzh7h+auHmlAcjUblCtPb28vVq1cZHR2luLhYXtPpdMpd18SEVc+ZTCZlKcTXCS+MmKlUipmZGW7fvk1nZ+djWyy/SAgp53K5qKmpoa2tjbq6OqnaZDJpQqEQNpuNyspKHA4Hc3NzrKysYDabqampkfH1RCKO1ZpdckUEbWBggMXFRWKxGMeOHeXEiZN4PG5aW1tpbGykurqayspKiouL5YauQg3I70m5E3kBexHPjZjqkhWNRhkdHaWrq4tIJMKlS5d2PO0q3/AQvyvUS0l1QKvlFGIXN5fLRSIR486dr0gkkni9RdjtNoq8XhwOJ2azQSoVJxwOMzKaYmxsBE3LEA6HiUQjBMoDtLS0YrGYmZubZnl5EZvNTDAYoKKiHK+3iNIyP5WVAWx2Ox53tiV4Op0bZQJyntPLEsXZCp4bMUX4LJlMMjk5yc2bNxkeHubQoUMUFxfvWmfajSB8gYlEglgsxtraGisrK6yurua0T1xYWGBlZQmb3cLDqXES8SS1tVW0tLZiMhtkMkkSiSiZTJJINMTs3BSzM7MsLi4SjUXRdR2v10t9bwN+v59QKIyuaZSWlj+SxDVYLGC1mnC5vFgsNjBA07J7YRqs661iYqkG5ouoFHgeeG7EFBbm9PQ03d3dTExMPGap77SzWnXRCFfK2toay8vLkoDhcFj6KldWVlhZWZFLp9vtlvuFezxOvMVFpD0ZTGYTsVgEXddkckoylSCdTmIyQXVNFS63U8bxs1sCrrAaWkHXQc9ozM3NsLyyzPDIMEVFHoqLi/GV+Ckp8eHz+fB6i7BYzJhNFnjBNVUvAs+FmEI6jY+Pc/PmTcbHxzGZTHi9XiorK3Mq8nZKXxKZTUIihkIhotEoMzMz9PX1MTU1lRMKLSsro66ujuPHj1NSUkJJSQk+nw+3243VasFqM2OxGKytrRGNRllYWGBubk7G1NPpNF5vMc3NzbS2tkpCiuwqXdOJxbPjWFhYZH5+jvHxCe7cuUMsFpUToby8nOamZpqamnE4PPj92dwAsUfSHwqeCzFNJhORSITu7m4GBwdJJBJyD57y8nJgPct9uwaQmATxeJz5+XkGBga4e/cuAwMDRCIRuXHSqVOnaG1tlZuhCn3N4XCwtrYmEySy50uRTmUwbGbcbjdut1tuFRMKhbIRMm8RVYEqKioqZNMAkRsgzuN0OvH7/dTW1uKwOzCZTaSSKdYia8zOzvLw4UMePnzItevX+NWvf0VkLUVHx0HOnDlDS0uLdF0Jq//rLDmfGCvPx9M+DLWk1mw243Q6OXbsGOl0mq6uLtbW1qiqqpJ7+oicyvzzq1EVcf2NljPDMGQLvVu3bnH//n1ZByRKVH2+7FJps9lIJBKk02m5v5DYdEpEtMQ5MxkrmpbCbFl/HpWVlXg8HkKhEJlMRpYLCwe62WyWW0qrkRyHw4GhZ6V5OpOWCTFFRUW0tbVJa351ZZX+/hG6u3v4+c9/zszMDMFgkEuXLnHp0iXa2tpkUs1m0ST1HbxMMBmbmML5NTNPCqupEEupiOjouk5PTw937twhHA5Lgly+fBmPx0MqlZJZO4XOlb+tijrGubk5+vr6uHfvHgMDAzgcDlpbW+ns7KS+vl66XfKzm8RLzS/sVxs5ZI/T0Y0MhpFbXqHWm6sZU0KfFZ6IjTYBVZspCHfZ+j2DCRvxeIpwOMTa2hoLCwuMj48zNTUFQEdHBydPnqShoUFmc4kxiZVD+D9fNum6q8QUmUAmk4m5uTmuXr1KOp3m8OHD1NbWAlBaWipntqjWU88hCvPFlnpCGsViMQYGBrh+/TqDg4NYLBbq6upobGykvr5e7i2U1RGtMsUun/iFpEl+RxEDHV3PJWa+JBe/E99X49aFiJ/fMeTxcZgxYQXM8vmkUimi0SihUIjFxUVmZmZYXFzEarVSX1/PoUOHaGxslEku6rlfNqNpV4ipnjKdThOLxfj9738v3UMXLlyQmz6pVXr5+qV4+YK0yWSSmZkZhoeHGR4eZnFxEbvdTnV1NXV1dVRWVlJeXi6TGoQ0VO8n/3YLScxnIaZ6nDiXGLMIU+Y/M7XyU3WU5xLdRCYN6118TBiGjrhcOp2S7q3Z2Vmmp6fJZDKUlZXR3NxMW1sblZVB7HbbS7mcb0rMJzUr3QjqKTOZDFNTU/ziF7+gqKiIS5cu5SSDiLKIQrqSml0zOjpKf38/Dx8+RNd1ioqKKC8vp66ujtraWrxerwxpZjKZnMwmMSaRfvek+8lPZSu0lAspln8uoU9uREzVWyD2WxffWf9kz5dO6xiGCQyyLiPZKZlHKkL23tbWssbTxMQEs7OzpFJpysvLOHjwIB0dHZSVlT8KkZpQb1WN+e810j5zEsfTLgeqTjgyMoLVaqW9vV2WPYiXqi75wvgQDyyVSsltiIeGhlhbW6OkpISDBw/S3t5OMBiUyQz5+xpuFHPfyGja9DiTGbNhQtdzv1soWiWkrVBh8pdyldD5CcDCXWYYOrpuoGkZ1NNnCZ49dzqjo2lmdMPA7rDQ2naAmpogM7MzTD2cYnFxkdu3bzI2NkzHwYM01Dfi95fl7Mmp+nj32lK/qcTcKsSLSafTjI2N8eGHHxIMBrlw4QLV1dU50kFIOJE4rOs68Xic1dVVxsfHuX37NrOzs1RUVHDs2DE6OzspKyt7Ypa2eo2nGWt+il6OSvGUS7m4Z/V3hQwuVZoK5IdD1ZS57PfIOtzNFsB4tCpo6Lr2aMxW7Hab1NOXl1e4e/cOAwMDFBV5qaysoaPjEM1NB/B6i+RkEM9fjHGvSM5dI6amaSwtLfHTn/6USCTC22+/zcGDB3O6buQntWqaRjQalVV+Q0NDWCwWTp8+zblz5+SOr0+TCLtXiFlItytUHpJPTFWaqseI41R1RVRA6vq6RW6xWHE4HESjUe7du8/Vq59TVlrB2bNnOXToEGVlZTmtYYQE3SuJNLvmYE+n00xOTrK0tERnZyc1NTUyU0Yk4grHszj+4cOHfPXVV9y5cwe73c7rr7/OpUuX5BZ9sH0H/PNGIV00Hxvdz2auMzVECbkTQHgyhEF1/PhxmppaufbFdX79619z//59rly5woEDB7BarY/tgLwXsCMSM/8hGYbB0tISH330EQ8fPuS73/0uVVVVctkQ7WFEIm0qleLTTz/lk08+wel0cvnyZU6ePClLMADpqAaeyv2xUxLTMIyCEhMoKDGFWpI/DhWFsvwLScz8TCjVR6r27RTkEknWiUSCSCQi8zSj0Sgej49UMs3w8AjXr18nFApx4cIFXnvtNSorK3OMz3w31osQBNsmpniYqpN4bW2Nrq4uPvzwQ958801Onz4tfYmCjOpy/1//9V/Mzc1x7tw5Tp8+TVVVFQ6H4zEXC2w9iUHc5kYVlvnLr+qqypJSA1Ou5Csk0R5zNW1gWAkDUP3kTyYRdhSkSafTJJPJnD5K6vIr/hXLvGwvqGmYTTa0THbMy8vL3Llzh56eHsrLy3nnnXdob2+X70jot0JNeBHJ2zsiMdXkVV3XGRkZkc7073znO5SWlsqHJepUlpeXuXXrFteuXcPn83HhwgWamppkuHA3UMgpXgiq9Mrem4bFAhZF8SkkCQtJ380gVo+NWoTnE0I1jJ40DmFpyz8ZFlZXwxhGtho1Ho8zMzPD1FTWgj969CgnTpzI8XSIMbwIg2hHdEyxfJnNZsLhMOPj40QiES5evIjf789eSLFOx8fH+fTTT+nr66Ozs5Pjx49TU1OT00R0LyEr4UxYLWYM1n1/W+05r5JefXb5lZeFxpGvYxcykh4/h+q2yuYteDwevF4vtbW1TE1NMTg4yODgIBcvXuTo0aN4PJ4X2lN/R4gpdMZkMsnExARTU1MEg0GZ/iVixvF4nL6+Pm7fvs3S0hJHjx7lG9/4hpSoexVZIunZpVx5TwZbe2kqMdWoV6GS4Hy1IF9iit9v9jOQUzME6x4Rv98vo0PDw8PcuHGDhYUFDh/upLa27oU1T9iRq4rZODc3x8jICKlUiiNHjsgabMMwZCuT7u5uMpkMp06dkg3pxUPaK1CXx3UXjU4mk0uI7RgGqmEjdG+hQhQiJKxLRzGJhe75pFXGZALd0LLOecNA09PrUbVUnEQiRlNTA4FAGXfv3uXWrS9ZXJznwsULtLS04nQ4MdDlpMx+d3ff17aJaRjZeHcqlWJycpKVlRWCwSD19fVSEV9ZWeGrr76S/XXOnj1Le3u7rJ+G3OrBF+0OUrOL1p3OBpget663CkEo1dMgri2scuHGUSWryFbKj62LZ6eOSx1fMhnDZNYxG2AyaVgsVsxmE4lEBkwaGS1JIODnzNmT3L9/n5mZh3z++VWSyRgd7QdxuhwYuo7JZMZsFrmgu/eetk1MMduXl5eZnp7G4XDQ0dFBIBBA0zQWFxe5evUqExMTnDhxghMnTuTskAAvtlxgI+Mh37ENJtihMWqaJlu9iPOrW1Crv8t3K6ljFMcWynLKJ22W2Lq8vq5rj6R1BrM5G0NPpZOUlfl59dVXmJycoLu7h//5nw9IJRMc6uzM+p6t1kfRp93Ftq1y0Ybv+vXr3Lt3j+bmZr7xjW9gsViYnZ3lJz/5CZFIhHfffZejR48C2aQMh8MhU9nkYJ4hrW4rKGSV58fZxTjyvgk87i7a6PzP+kgNw8jpwak+A9VIEn9TdU0Rscm/J/X3hXy6664wPUePjMfjMjdW13VpE/zJn/wpZ8+cw+l0YLM5sVi231FvM2xbYtrtdrq7u7l16xZ+v5+Ojg7sdjtDQ0P8+Mc/JpFI8M///M/U19dLB7vD4chxSbxIFLKuhaTaTSleiEwisVcYQmqCiiCn+OSPP/+e1EmYn1UlVCyx664gocjEF01vTSYThw8fxmQy8X/+z0/QMhkuXbqM01m0a89FYEvEVGOr4XCYsbExUqkUFRUVuFwurl27xq9//Wvcbjc/+tGPZGRBOJVFzY8oDYB1y/55L+liycx3sG8VhSRmIUOmUHRIXFeQTeytJD6q/i0ML7H8i7+L/+dH1/K3HRQTTyRQizGIySCuDdDS0sLbb7/Nz///n7Oyusobr3+TioqgHKtqvO0UnomYhfQaUdZQU1NDY2MjDx484JNPPsHv9/P2229TUVEhl/twOEx/fz/T09NUVlZy9OhR/H6/rOEWmxE8T3IWsqy3shzDxg78J95Tnj6bnzKXb5Wr4UpRTiE+4p7yw7aFxibSDEXiibi2KqUh25Hk8OHDRKIRenq6sVhsvHLpG1RVVUtHvqZtb0+lfDwzMWE9ZCeam46OjhKLxQiHw8RiMdmmura2Vn4nHo/z+eefs7q6SklJiWxgf/78+ZyH+ELisjt8zXy1YCOneP7xORlNj/TIfN3Q0HO3RBSEUj/imuryX2jCqC4r9drq/81ms8xCunD+Ai6ni5GREew2FxcuXJR7Oe00nnnNkv6vZJKhoSFmZ2dpb28nkUhy48YNQqshTp3MlsaKB2qz2ZicnKSvrw+bzcbhw4cpLi7h/v37jIyMSD1nL/kydwpqYsZGn40iLIIwOcnGeQbNM40l72fhetrsI9QA0Ymvra2NQHmAwcFBbty4weLiojzXTuKZJKaa5RIOh+nu7qa4uJjSUj+pVBJd13C5nMwvzFG3VoevpOSRK8LE6OgIhqFTURGgvLyMpaVF5hfmGBoa5NChg4BJJr0+f4LmvzIDUF68ycC0xSiPkFaFMow2HVGePzffgBHH5EMsq2qsW/iZ1QmguqhUmwHW9xAV5BcbhyWTCRwOB4cPH6avb4De3gfE4jEuXbxIfX0D688NMJkwbcPP+czENIxs67vZ2VmWlpbw+YoZGOyjpqaas2dPMTo6yvXrn2OxmLj86iuYzTY0LcPi4hyZTJL5+Wm67t1menqGSCRMLBYBNFKp9KOmAw4MY/OWKE8jLQo5mQvDAPJfeNbPJ3lpMsD8uDv5sWVWWVbzj8n3iz6NXpvvDjIMA4P18+VnXKneBDU4sP63dXVWLSsWe8+rESX1XtaJawY0ysr9HDt2hEwmRVfXbUCjqMiN3+9DNx4V2pksmMwWthohemZtNZPJMDs7y+3bt7FarUxOTlBaVsKpU8dpbmqmuroSTU/x2eefUF1TwbGjx9C0FLH4GlPTEywtz9Pf30s8EScSWcVT5AA0ND2FxeoEHlfSt0LMQt97HI9IadJQpaZBGt1QdUAwG+ZHL2Z9DIXIlC/tBTmeNN5CWe35xoRhGGS0DJqea+yohFSNufxsJItlPY1O7RQnJoCQqKrkFPdgsVhkUCASWcNsMXPq1HECgVLudt3F6bDy+huvP+p+Zwazgckw5TyzZ8EzGz/z8/Ncu3aN27dvEw6Hqa2t4rXXXqOpqQnd0KkMVnLx4gVmZ2d47733qKurw2634/UWcfLkSc6cOUtbaysDgwP87Gc/y3a9MOVW771oqOHR3UC+haxKKPWawpuR/11QJp2idwqICaM64VVjSfwrLGoMI2dDLwF1mVevLwIjGTI0NDZgtpj55S9/ic/n49TpU7JduW4YWLb4Xp+JzolEgvn5eSYmJh4t4z5+8IMf0NHege2Rsmyz2aisqOTs2XNMTEwwOjqK1WqlqamZjJaR2xAnU9ltVLL15aJib2s3sdMQEkIYADudkyiWzXzjJ38iiNxV8VE7eshjDSPH3STOLyJJosxCJWS++8lgPftIlECr9w+5JI1EIpLwyWSS6upq/uRP/oT/+//9X+7du0cinsZs3l73jydKTHU2i51cx8bG8Pv9/N3f/R31DfUAaJpORssq+m63h0MHD3Hu/Dk++eQTmpqaqKmp4datW3Tfvw+GQW9vL/F4HL/Pj6HvnVoTeHw5LrRsb+TaepKULeRgF+fL/znHWjeQSq7JbM4JChSS7kIi5ocs1WW6kNNe9Z2qUlVVEzRNk11N7HY7mUyGhoYGTp06xdWrVykrK6ehvhG73YnZasEwnt0lZ/mXf/mXf9noj+pMjsfj3L59m9/97nekUin+4i/+gqNHj2K1WTDQMMj1p4m2eh988AEdHR3U1dbhcrtIJBLMzc1hNps5d+4crW2tWG1ZSWAxWx/pJIVfeL5S/jS+z3zjI/d72QpIw1i3nNXoifryCkF15WyUAqdeT9UjRbMDIZELfU8lRzqzXlym592PSDIW/xf3LeLgJSUlOeqJWObVojWVyOpzEERcz4g3SCQSJBKJHI+DYRiUlZUxMTFBZG2N8vIAfn+296mu50a2ngZPlJhCPxkfH+f69essLS1x4cIFGUNNpVJYrbkEEd8JBCrwuD3MzMzQ3NzC4c7DVFdXZ31iNjv+Uv/6rr0m8yNdaQsNCTZAoe8Vkiy6kXVzPCsKnWsjSahKynxDR9UH1e+JfdsFMcT+7OpxIqaukk64eETdj1rIpxJOtF1Ux5bvjBfEUw04MQnF9opCWJSWltLe3k5PTw9F3ju43EVUBIIYhi5zbp9Wcj6V8ROLxejv75cbQZ05cwan0/noYo97q7IPB9wuF42NjUxNTRGLRqmsrMDtdqEpkmjdV/hU41XOv/WSBuU3ZK3yZz4VsLXQpSqxNjtX9pg0hgGalnmkL+bnYGZJG4/Hc76rVlkaRnZ3DEFy9fzqdTdeFZCri7CwbbYsbcREERNA13Xq6+sZHx+n98EDir1+zp4twu12ywnxtKUzT2wRYzabmZycZHx8nLKyMi5evEhtba2ccRaLASYdVeJkH54Jq8VOY1MTPQ96sk3y9XJ0A3RNR9N1LGYzFrMFi9mCyWTGZLKQZcnT90ZSx7oVZO/RkjP+Qq/o8US4R+UWOUcLPezxb5pMWb+oxQJms17QFfS4H3OdkJqWAUyyj+f6MZrc+VicRxgyIqE4FothGBs3LRPky/XDmh7dmxkDDQydrK1sPEoytsi9ilSpKvJx79y+y4MHPQQClXR2dj5zo9knNm4NhULcuHGD2dlZDh06RH19PbFYDOCR4pvCQEnD0rOkM2HGanXgcLhYXQkxMzOLy+V+tGQrDnBEaYBI188l5kbLo7p0wXpMNz8trFCMONdBrWcd6CrBTLkuHbPZDMbjGUGpdCpruKn3k/fwhYoiljOxjFqsj4wXw0DXDbJdNB6/T6n7KQkaFosF86N2MSaykiv1qKRX3RU426fIIBaNk0pl5N/S6cwjois+UEwYZP8GBmazBbM5W2WZldzrDb+sVgtWiwWT2YzZZMVkMUinUkSjcZLJNCUlfsrLAwwPj/Hll19SVVVFIBB4ptVlU2Lqus7AwACff/45uq6zurrKzZs3ZWuSrJ6RItv8KWs2CheE1ZrtlDszO0NoNcq1L75kaHAUq9WGxZJ1VqtWYfZ9Pi4tH19+ydn6TiQ6OJ1OgsEgq6urrK6uSqmi+gLN5myFoKr8Z5e93OZVVquFdDrzSBLxqHGA+dF9i2djkEol0XQdszJRUuk0IlMcwGa1YbXaMJlzo1mWRzHojJZBy2gkkkkyar242USxtxiL1QqPCJHVNTNSMjnsDhwOB/FEnPn5BQxDp6TE96hlY7bddrYZrvVRax5dLr355RuZTAan0ykno9VqeyTVDRKJpBw3JrA/cinpuuor1R51Z86WbESjMVZWVrl37x4tLS1cvnz5saTkzbDpURaLhaqqKjo7O+nv7+fmzZtEIhFJTMMwsNnsys5cxqPlKkuArDVoxel0MTAwSH//QNY/ZrFitqy7JOTLMD1enmqxWGRvHgGRJqdGP/x+PzU1NYRCIbk5lN1uzyG12Zzd/VeQXbSqyU8gyeaNZkn/yJGC0+nE7V5PkM0uoRkyj150ofrw7IQxcLksWBCrQtbtmNF1NM1A18AwTLicbsyuAj2OUuuZ64lEkrW1Nbn3pnB2u91u0unsBF1biwBIvTM76c3Y7TZ5X1kLm0dVBFqO+8fQDdKZtGyukEqlSCQSOeMSz9Rms+Nw2LFYrFgsuVExq9VKcXGJ3JVkXWA9HTE3La2IRqM4HA6SyaQMR+W3TVZdFPnId++I458VhUKShaA2TX2WRqVPO6Zc/QxyEj22eP6ciZm/WhTQdlULWhCkkP6mnlcYQhu5s1RPwWPtcTa5v6d5bsJ1KGLy6qasm35vM2KKZTA/X1IdkBpjVQeTTwzR1kT1uT2tzvEkHVMszUKHEop4oQcn/HFqZs3jRsc6scVLK+SHK1SjU8hRnv87QQLV/1loHBvdt/j/Rl6BQu9IjXurz0ZNSlYrMdVzbPaexPMp9LxV1UW1BZ4GT1zKxck2mh3iJRf6vXpj4iU/rfTLP9dmP6tj3Ewy5y+zhcaz0bGFVoZ8Czd/dSh0LvXY/Mm82Rjyx7LRtQp9N3+FUye2eg71/vK/o0KdEE+6h/xxPy02lZgq47eLjW5gp5bC/BvfSCKr97TReVXpop77acbxNATLfxZPQ658POmd5F8jP0VOPe5Z3+9GpNzq8ymEXWncuo99bBdfv1qGfXwtsE/MfexJ7BNzYZUjBgAAADFJREFUH3sS+8Tcx57EPjH3sSexT8x97EnsE3MfexL7xNzHnsQ+MfexJ7FPzH3sSfw/eJU5ZRPPxkIAAAAASUVORK5CYII=)
A bullet of mass
is fired with a velocity of 50
at an angle
with the horizontal. At the highest point of its trajectory, it collides had on with a bob of massless string of length
m and gets embedded in the bob. After the collision, the string moves to an angle of 120
. What is the angle ![theta ?](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKYAAACkCAYAAAAdQFV8AAAgAElEQVR4nO2993Nc1333/9resMAugAUWvRCNBHsvoqxIohw7iaJkLNuZOIl/SzKT+G/If5HMJB4/mXHm+U7s+dpjayRHtiyFKiwSC0iA6J3odRfbd++9zw/Lc3B2uQBJFBKU8Z7ZIQHcvffce9/ncz79mAzDMNjHPvYYzC96APvYRyHsE3MfexL7xNzHnsQ+MfexJ7FPzH3sSVhf9AD2sXeg6zqGYWA2mzEMg2QySSwWw2QykclkWFlZIRwOY7VaCQQCBAIB7HY7hmFgMpkwmUw7NpZ9ibkPCcMwJDkNwyCdTpNMJjGZTFitVpxOJ7quE4lEiMViZDIZ+b2dJCXsS8x9kCUWgKZp8udEIsHy8jKhUAi73Y7b7SYajWIYhvxdIBDA5XLJ71kslh0b0z4x/8Ch6zq6rmM2mzGb1xfQRCLBwsIC8/PzuN1u7HY78XicaDSKpmnY7Xas1nX67EvMfewIxLKt63qOfphOpzGZTITDYRYXF0kkEgA8fPgQm81GJpMhGAxSXl6O0+mUy7hK6p3APjH/QGEYhlyCzWYzsViMqakppqamqKysxO12EwgEMJvNZDIZotEoRUVFLC4uSn3TarXKc+w09on5BwIhGQXUFIn5+Xl6e3vp7+9naWmJ8+fPc/78eRoaGtA0jWg0Snl5OVarlVu3bpHJZCQhTSYTuq7v+Hj3ifkHAk3TJDHFv4ZhEIvF+PDDD/nss8+oqanhzTff5OjRo3g8HiBr0Hg8HtxuN1arVbqOHA6HJKSw5HdSz9wn5h8IxLIrSKRpGul0muXlZZaWlvjWt77FK6+8Qnl5+WP6omrk1NXVsbKywtraGpqm4fP5gCw5d9IqN+2nvf1hYWVlhWvXrtHT00NraytvvfUWmqZhs9mw2+1PZcTcunWLW7du0dDQwJUrV9B1PYe8O4F9ifkHgnA4zBdffMEXX3xBKBSira2NtrY2HA4H8XgcgGQyid1uf6Lkq6ysxOFwsLi4yPLyMm63+zF303axT8yXHKpuJ3Q+k8kkjRtBlgcPHnDv3j0qKyt58803aWhooKysTEZ1rFYrqVSKp1lAKyoqqKmp4eHDh0xNTdHZ2flU33sW7C/lLznUECIgfYrJZJKZmRlGR0dpbm5G13WWl5fx+/0Eg0FcLpc8XpBb0zQsFssTjRhN0+jr66Orqwuv18u3v/3tHfdl7kvMlxz57ppUKsXKygqDg4PcvXsXm81GfX099fX1NDU15Ug24VgXRHxaPdFkMhEMBonH4zJevu9g30dBCGIsLCzQ1dXF4OAgmUyG48ePU1lZidlsziHwdlw7JpMJn89HW1sbkUiElZUVysvLt30PKvaJ+ZJD13XW1taIRCIUFRURDoeJRqM0NTVx8eJFKioqSKfTOUv9dqGmuS0uLjI3N8drr72GzWbb9rkF9om5hyEIkE8q4YfMZDIsLS0xNDREb28vR44c4fDhw7S1tWGxWKSUNJvNO+r8FuqDpmksLi5y69Ytjh49SkVFRcHxbgX7xNyjEPmQFotFJlxYLBYsFguaphGJRBgZGeE///M/iUajXLx4kUAggMPhwGazSVLspNNbQBg6Ho+HqqoqfD4fw8PDBAIBIGscbXcy7BNzD0N1/wgJKKTR0tIS77//PsFgkG9961s0NzfjdDp33AjZDFarFY/Hg8Vi4datWxw+fJiioqIdkc77xNyjEP5FISnT6TT9/f1MTU1RUVFBbW0t7777Ln6/n5KSEqnfZTIZdF3PkZo7DeGeMplMeDwe6urqGBkZyUns2O6194m5hyGW8+npaW7dusWdO3fw+/3U1tbi9Xrxer24XC4pRVXdbrdICUhjymw243K56OzsJBgM4na7c9xX+0v51wCFDAaTycTQ0BBXr14lmUzS3t5OW1sb9fX1MklX/Y5hGE/lIN8uhEohVAyfzyd9oJqm5RS0bXUs+8TcA1CTdgFWV1eZnp6mpqYGm81GRUUFlZWVtLW1EQgENnTLCP1yt4kpDCphlKXTaQYHB/F6vbS3t2O327d9jX1i7hEIS3tqaoqenh5CoRB/+qd/SnNzMw0NDdhstidaurtNyPzrCAmt6zoTExNomsaBAwdwOBz7OubXBSsrK/T09NDV1cXs7CzHjx/H7/dL6fO8SPc0yA9rOp1O6urq6OnpIZ1Oy2O2M+b9uvIXiFQqRSwWI5lM0tPTw2effYbZbOaHP/wh77zzDm63Wx67k5Gb7UKtPwdwOp20tbWRSCSIRCLSat9OycW+xNxlqK6V/MhNf38/MzMzNDY20tbWRmtrKz6fj6KiIjKZTM7L3W1L+1mQb6AJI8hqtZJIJHLcRlt18O8Tc5ehFoGJMOLi4iLvv/8+H374ISdPnqSyspKSkhLS6TSpVEq+7J1Ovt0p5E8Ss9mM1+vl3Xffpbi4WI57O2PfJ+ZzgFjyUqkUDx484Gc/+xmapvGDH/yA48ePU1FRwfT0NCMjI3i9Xvx+/44n3u4mTCYTNpsNTdMIh8N4vV6cTue+H3Mvw2Qy8fDhQ5aWligqKiIQCPDGG29QXl5OXV0dXq8Xm81GKpVidHQUs9nMwYMH8Xq9L3rozwRd17l//z4Oh4Njx47hdrv3/ZgvEmrURTiWxcuIxWJ0d3dz7do1AC5evMjRo0cpLS2VcW21k0U4HGZpaYmpqSkOHTqUk12kvuS9omuq0HWdWCxGOBwmk8lsWyfeJ+Y2IAijljZA9iUNDw/z5ZdfMjg4iNls5tChQ1RUVMisHMglmGj5Nzc3R1dXFwcOHJCuItUB/zwiO1uBMHRWV1dzmnNtdax7T7N+yaAW+wsdK5VKMT4+Tm9vL16vlytXrnDlyhWqqqpyLFYVKysr8nPv3j0WFhYAChJ/r8IwDFKplOyJtO8uekEQZBFZ5BMTE8zNzXHq1Cnq6ur4zne+Q21tLT6fTyZkFFridF0nHA4TDodJJpPMzc0xODhIVVWVPEZIyr0oLSE70UpKSkilUthstm072PeJuQ2Idinz8/Pcvn2bq1evYjKZ6OjooKWlBbPZTDqdzumoJnyTqislk8lI0jocDtLpNN3d3Zw5cwaHwyFdL3uVlJCdOE1NTZSXl+PxeLbt5ton5gbIJxM8vvwmk0lu3rzJRx99RCgU4vz587zxxhvSlwfIvEg1GpK/LKfTaUKhkDQcotEofX19LC4uUlVVtSd9mfkwm80Eg0GKiopkj6N9ibnD0DSNRCIhE3V1XcfpdD4WxRgbG+Pzzz/H4/Hwl3/5lzKzptBLEb6+/O69Qqo2NDRw8eJFAFpaWmhubsbn88lrqhNlL0pOTdMYHR3l008/5Zvf/CYNDQ3bOt8+MTeA1Wolk8kwOjpKOp2mo6NDNgkQSKfTVFVVUV9fT1tb24akVKFKYMgSzuVycezYMWnNl5WVSVVgL5JwI2QyGWKxmMzJ3E/i2AVYrVZisRgPHjzg7t27LC8vP3aM6sIRDU63ei2v14vD4SCVSuF0OiXJXybspPdgn5gFIBzeq6urjI2NMTQ0xOzs7GPHia1EhItkqwkLgoDJZJJMJvOYZH6ZsFPk3CdmARiGIZMtFhcXmZ2dZXx8XBIHkHqnUPSF1HxaKZff2iWTyZBMJrFYLJSUlMhjCn32GkQAwOPxEAwGdySDfZ+YBSC2E5mfnycajRKNRhkdHWVlZSWHTFarVRLyWSxn1doXutja2hqJRILi4mJKSkpyUuX2MilhPT8zEAhw4sQJiouLty0194lZABaLhVgsxvT0tFTmHz58yMOHD6U0ENJxqy9A7Y6m6zpzc3MkEgmqq6tlG+mXgZSwXmpsMpmoqKjA5XJt28W1T8wNMDc3x/j4OIuLi0QiEaanp+nr69vRRviiy0YymWR2dhZd16mrq8NkMj11r8q9ADFphKEYiUT2Q5K7gVQqRW9vL6urq7J22maz8eDBA+Lx+LYlQr7DfmFhgZmZGVwuFzU1NVJn242t8HYLmqbx4MED7Ha7rPvZDvaJWQBms5nDhw/T0NDAwMCArOkG5JIFuYX/z0pUNTTZ3d1NNBqlpaUFl8slexaJpljpdFrqs6LkQoxDxOALjUEQXHXs55dF7ASETj49Pc0rr7ySU6u0VewTcwM0NTWRTCYJhULE43E6Ozsf8y8WSkV7kpRTpaHVamVwcJD+/n5qa2tpa2vDarXKjsC3b9+mqKiI2tpa2Yp6dXWV4eFhxsbGsNvtnDlzhkAgIAMCY2Nj9PX1kUqlOHDggHTch8NhPv30U1ZXV2ltbaWzs5Pi4uIdeVZi49OZmZmcnNH9kOQOw2w243Q6gXWp4nA4ZB7ldiBcS4ZhsLq6ynvvvYfFYqG9vR2/3y/1ywcPHvCv//qvvPbaa5SWluJyuRgZGeGzzz5jbGwMr9fL1NQUY2NjvPvuu1RVVXHnzh0+//xzpqen0XWdnp4enE4nra2tDAwMsLa2JrOgysrKdoyYYpMqj8eTU1KxT8wdhlgSxXIr9sfZSaRSKT766CNWVlZ47bXXaGhoQNd1xsbG+OKLL+jp6WFsbEwWsCUSCfr7+5mcnKSlpYVDhw4xOTnJjRs3GB8fx+VyMTQ0hGEYvPLKK+i6Tn9/P1988QXV1dXMz8/L5lsmk0nuEbkTsFgslJWV8cd//Mc0NDRgt9vl89qqLv5SEDO/aRTk+gLFzzuF/DJbsfQWGtdGYxO/E24fUUZhGAaRSITbt2/T09PDqVOnOHr0KF6vl1QqxdraGktLSwQCAZqammSbP8MwKCkp4fjx45w4cYJgMEh9fT03btxgdXWVyclJ1tbWOHDgAFeuXCGVSuFyufjkk09YXFyktLSU2dlZ4vE45eXl0om/VeTH+5PJJPX19fj9/h3pybnniZmfwZ2/TUj+MYVqnrd63SdJSzVTWx2jOjZ1qzxN0wiFQvT09HD9+nXa2tq4ePGi3NbEZrMRDAZ58803KSkpYXV1VbqNHA4HR48eRdM03G438Xic0dFRlpaW5LFipzKx705NTQ3RaJTl5WWam5tJJpNyswDRZHU7z0YYfrFYjDt37uB2uwkGg38YxIT1lK/85gGqxFStU/F78bK3ek2VbIUInk9edYwCwrKORCIsLCwwMDBAV1cXtbW1vPXWWzmlularlUAgQCAQIBKJYDKZchKNRURlbW2Nvr4+/ud//ge/309jYyPT09NyPGLsoq9QOp3G5/Px+uuvb+lZFLpvtQnY2toad+7c4ejRo/K5F8o7fRa8FMQUMzCRSEjXibqRu2EYskJP7XK71ZkrHq5w0WzU7kT8TbhwBBHUJgdi6e7v7+fatWtMTk5y5swZ/vzP/1z2kxTZ6/n6mBp/F+dMJpN0d3fz3//93ySTSf7pn/6JYDAoI1TxeFyqH4CM5+80VMEgqjvVZXy7wYE9T0xVUqVSKb744gusViuHDh2iuroaTdNYWFjgN7/5DR988AHV1dW8++67nDhxYsvJBJlMRhJb6IaF9uUWhBFdfIEcv+Hq6irLy8t89NFHXLt2jaqqKv72b/+W48ePy/vaqMmpkPZWqzVHEnZ1dfHBBx9QWVnJ3//931NaWophGBQVFeF2u6WxZLFYiEQiJJPJnP6VOwkxUVZXV3E4HNTV1eXsR/m1tcpVn18ikeC3v/0tv/nNb2hpaaG2tpbq6mqWl5e5evUqd+7c4Y033pA/WywWTp8+vaUXotaIqxnk+RDkVaVjPB5neHiYO3fucOPGDUKhEIcPH+Yf//EfaWtrw+PxSF0vP5+z0BjUz5dffsn7779PJpPh7bffJplMyiYJLpcLt9vN3NwcQ0NDlJSUMDIygmEYeL3eHS3PUMck0v06OjqoqqqSz+NrX/NjGAahUIhf/epX9PT0kEqlKCoqktIwFArR29vLt7/9bY4fP04sFuN3v/sdS0tLrK2t4ff7n/maalRFqAyFliaHw8Hy8jJffvkln332mSzhTSQS+Hw+Tpw4wYEDB2hsbCQQCEjfaL6eDI9LF7PZLBts2e12NE1jZmaGyclJ4vE4P/7xj+XLP3nyJFeuXOHIkSP87//+L//2b/8GQFlZGd/97ncpLS3dUWKazWapLthsNlkKovbF3K6XZE8TU8w8q9VKa2srHR0dXLt2DYfDQSaTIZPJSPdKbW0t5eXlMi9QlMNuhZjqw90sx1LooTabjaKiIkpLSwkGg/h8PsrKymTjfpfLlaPvPs3Ls9vtvPrqq9jtdtxuNxaLhRMnTlBZWfmYh0Jcq7S0FF3Xqa2txTAMqqur6ezszNntYifcauK5iH2GpqamOHLkyI667PY0McVyYbfbOXr0KE6nk/7+flKplJyxiURC6lTiX7/fL9uU7Pb4fD4fZ86c4dixY3i9XkpKSnLKV7e6rFksFg4cOEAikZDnaGhooL6+Pud8qo6qaRrNzc3U1dUB4HK5sNvt8lns1J4/guSJRILJyUkGBwc5cuTIjpxbYE8TE9bbKTudTqmTiW2MIfsC1Z0bICtBgB1JJtgMIou9srKSjo4OOSZhEG2HDCaT6bG8zEKuL0FM8a/dbpfPQ42+7GRhmxAYi4uLTExMyFVjJ7Gr+ZiqLyuVSkmfXCHFXhyf7/8SD1RYviL5QRgMNptN7uAg3DXhcFi6lYCcl6Qq7epY1Ouq/6oWdz7E3zOZzGPRIVUN2A4h7HZ7Tv/1/I+QnmazWR6rGlMWi0V+fyeRTqeZnJxkenqapqamHd+BbdeIKRy7wrIeGxtjZmaGeDye45RWX2g6nZbkzU80FRGURCJBMpmUkkS8iNnZWaLRKPPz89y7d4/p6Wl5bjW0KM6r/pzJZOTEUV1DmqaRTCZJpVIb3mchp7/FYpFG03YJ8aRaIkFO4SEQx1utVmmM7LRKYzabiUajrKysYLPZaGho2LbfMh+7spSLlyvyDdfW1vjNb35DfX09Fy9ezNnEXXVGqw9QEFu8aJvNRjqdRtM07Ha7fAnl5eW0trby4YcfyqL7VCpFTU0NXq83hzTLy8s5UlqQJx6PEwqFcDgcBINBKX3zJetexWak3Q2IVUu05w4EAjt+rR0npiqdBObm5piYmKCurk6mRakOZjXRQfwr/GO6rkv3TSqVoqqqSh6jaZrspjY5OclPfvITkskkf/3Xf83Bgwel3iN6N3788cfcunWL2dlZ0uk0LS0tlJaWMjAwwMDAAJ2dnfzDP/wDTU1NO+b2+DoilUphsVjk/pXine+kE39XJKZwowhyTk1NUVxcTFVVlczQ1nWdaDTK+++/T19fH6WlpTI85/f75RbHHo9HSl+n08lbb72FyZTdwkNERlwuFz/60Y+kte50OnO2j9N1nVQqRVdXF/F4nO9973uYzWZu3rzJ3Nwcr776Kt/85jfp7e3lk08+obq6OsfnKO4pH3tZiu4mwuEwd+/exel0cu7cuR1RWfKx48RUJZ6YQQMDA9jtdoqKiqT/Syynfr9fxliFU1vojZAND66srDA/Py91KVWfE0t+MpnEMLLNBxKJBLquU1xcTE1NjWyYqmkaR44c4ciRI1itViYnJ0kmk5w/fx6bzUYoFJJ1PYLYbrebSCRSsI5FdGJT9eT8DKevA8Q9iX/v3r0rXUTqqraT2DUdU9XTFhYW5IacQjHXdR2Px8OJEyeora2V+mgqlcJsNhMIBLDb7SSTSaanpxkeHiaZTALrcWRd10kkElLJF9cT+2WLSaAaJMKKd7lcOBwOGbITbVri8bh8AcLqBwom1oqk272ug+4EhCH68OFDRkdH8Xq91NXV5TjvdxK75scUg11bWyMWi9HU1CSlkNAl4/E4Q0NDfP755xiGgcfjkUQ7dOgQbreb4uJiKisrZQN9QEpOkeomjKH8EJ/T6cTn80mSqmqEODadTpNIJHC5XDm6rpopJLwF+VAl49ddYorgxfDwMJCtiaqsrMw55qWI/AiLdnFxkUQiQSAQyOk9Lv4uWq4IK9tut0uiQdaZHgwGCQaDZDIZrFYr6XSaxcVFFhYW5DLS2NiYoxfmu3EgS2iRFpbvNlJ9lmpSRn5M+w8ZYtIeOHCA+vp6ueJsp2/TRti1pVwsb/Pz82iaht/vl8QRcLlcnD17llOnTkkpJUhjs9lwOBzSgBJJG7quMzo6yp07d5iampIP5fLlyxw+fDjHmZxPyvLychwOhzymrKwMt9uNx+PBbrdTWloqrX51e2Ph0N8Iqr/160ZgNYk5kUjQ0NCAw+GguLg4x/Oy591FkBtdiUQiBAIBiouLc16uiFQ4HA75HViPFqkJsuLvQme8d+8e9+/fJxgMUlJSQldXF++99x41NTWUlZUVJJHdbufcuXP4fD5KSkowm82cOnUKwzBkr6DDhw9TXl4u96gBHnN9qRDjy89g/7pBpPN1d3dTX19PaWmpTNsTtsFOY1eIqeqAVVVVvPXWW1RWVj52A+osE//PJ5W6pQhkiVJSUsKFCxc4ceIEDocDv9/P+++/n+NLUw0YyBoqhw8fzjm32nxf/FxVVSX9dLDehW2jRGE1pJp/T18HCD38q6++4r333uP73/++dO3tRvKxwK4RU/SO7Ozs3Pb5VKvX4XDw+uuvo+s6KysrdHV1ce/ePerr66UkVNtIbwdCSttstoJJCiaTCbvdLn2q4jtfJ3Lqus7y8jL//u//zp/92Z/JpXy3sSuxcmEtR6NRUqmUbGy6FYhSAbFkiF1exVbKv/zlL+nq6qK4uFhGiET20XYbqQp/qzDICh0n1BHhu/26LeWrq6t89tln1NXV8corr+xIi8Gnwa67i8SSvhUpoiZgiGVDJHO4XC65c+39+/dlh4qWlpac5X8r1xXfUQ2gjaTv19ViV8nn8Xh45513KC8v3/H0to2wqyFJ9YVu5+WpzvNQKMTs7Cwejyen389nn33G/Py87ASxnWuKa8G6D2+jDCOxR8/XYQlXDc1UKkU8HieRSHDq1CnZIx6ejx69axJzKx3QCkGQUiyVmqbR3d1NOp3m3LlzBAIBQqGQdPkICbad5UZ1Makd1wpBzT562YkJSL/y9PQ0vb29eDweXnvtted+b3s6gz2/LEHErj0eD729vfzud7/D6/WytLRETU0NwWBQEkmN7W712uqE2OneRXsVJpOJcDhMX18fQ0NDnD179oVMuD3fUVglp9AtT5w4wbFjx8hkMoyPj2O1Wjl79izl5eU7mkOpdvX4QyFmOp1mYGCAqakp6uvrOXbs2AsZx56WmALqjBVbw1VUVHD58mUSiYR02QCbZps/LdRUt82IqRo+agj0ZYOaOyAadJWWlsqk7hdxXy8FMVUICSpChfl74qj9GbcD1UG/WYa46DyRTqdz0vX2OtTAgBpQsNls0tgJBAI5uQPPEy8dMWFzq3CnSPm041CJ+zL5MIUbTrjDRCmuz+ejurr6sd05njf2vI65j92BMO5EPf7Pf/5zvvzyS6kaqYksLwL7xNwB5MfLXwaIBJTZ2Vn+4z/+g56eHg4ePChzGjYrKXke2JSYhWaMyKHMrxHfrPPu84A6DjUfcytQl2Y1JFrommo+6V7OLlKfiRhjKBTi+vXrDA8P88Ybb8hdM+DJ7XF2G8+sY6oDFWUL6gt5ESE6tZwikUiwsrKC2+2mpKRkW8ZIfj36Rn8XZSR72SJXJ4wqXMrKyvjGN77B+fPnKS4ultLyRYdaNyWmuqWcOli1tibflaC2JXneiEQi3Lt3j6GhIY4cObJtH5waltzo73tVQuZDvKdUKsX4+DgLCwtUVFRw/PhxALmDxV5xeW1KTJHRI4q+xM/io9Zti+ZWVqsVp9P5XIkplp2xsTFu3LjB2NgYwWBwR879onWtnYJ4R4ODg3z11VdkMhleffVVioqKcnJP94rk35SYgmhra2uMjY2xtLQkJabf76e1tRW73c7CwgKTk5MkEgmKioqorKwkGAwWTCTNf9Gqc/dJyJdgqrQyDIPl5WXZv1zUtW8nmVUd12aRn70qNVXpJyI6H3/8MclkkkuXLtHQ0EAqlZK+2L10H09cyg3DoK+vj1/84hcMDQ1JaXn27FkqKytxOp389re/paenR5bV1tfX884771BRUQHkZq3kE1GQXzyUfL+gWmoB2c3mY7GYzPEU5y4qKuL06dMcPnyYn/70p7In+XYg7keUdORDuFuEWrMXJI2AeDbiHUYiEXp7e6msrOTs2bO0trbKQj6hkoly5L2ADYlpGNmG+yZTtpFVbW0tly9f5syZM7Krr8/n4+7du/T19XHhwgXOnTvH2NgYd+/epbu7m9dff10STqSOCaJpmobFYpFNEMbHxzEMg/LycmkZJpNJpqamCIfDVFRUUFVVxfDwML/+9a9lhlE6ncbhcPDDH/6Q119/nUQisSMbhIrJI6I5hbKL1Oyj59GP82khxiMStufm5nC5XLz11lty9zL1+ezFaNWGxBR12SaTSW4gn0gkGBoawuFwUFFRgclkor+/n8rKStrb22Wd8cLCAqOjoySTyZz6n9HRUT799FOGhoYAZPVkaWkpw8PDhEIhjh8/zje/+U0sFgsffPABt2/fBrKZ1FeuXOHNN9/kBz/4AbFYLMf4EBsqqSHLncKTlri9tATC+qozMzPD+++/TygU4q/+6q+orq7OeS57kZACmy7lwg20urpKX18fo6OjOJ1OotEoJ0+e5Pvf/z6hUCin2lHc+OrqqpyxInE4nU6zvLxMcXExly9fJhwO86tf/Qqfz8d3v/tdJiYmGBsbY2xsjKKiIlZWVnj11Vc5e/Ys3d3dxONxzGYzFRUVkuzqMioavNbX11NWVrZj5HySJNwrklJgZWWF27dv8/HHH6NpGu+88w6lpaVy2c5kMlJg7FU80So3mUw0NzfjcrlkHXZvby83b97k2LFjOb2I1HobtQWz0BHj8bjMPD916hRTU1N4vV4aGhro7OzE4/GwsLBAJpPB5XJhtVq5efMm4XCYhoYGmpubKSsry0mWEHqSWjh24sQJPB7PlssA8t1fov0hIP2laoXki5KY4vQudMYAACAASURBVP0IXdJkyja4nZiYoKenh8bGRk6fPk1LS4vMvhLPaK9Npnw80fjRdZ3m5mYaGxvx+Xw4nU6Ki4vp6+tjcnISt9vN2toaqVRKxldF6pmmaTnp+BaLBZ/PR0VFBUVFRdhsNux2Oz6fT7ZoFqSuqKjgwoULWCwWJiYmmJmZoa2tTe4aK4iZb9FbrVZqa2u3vZyLPkmCkEJvi8fjOc3+xb0+j7S3/GtkMhlsNpvcVmVtbY2Kigp8Ph9nz56lqqoqp6nqi3aaPws2JaZwFY2MjOByuSgqKpJRDtEky+l0MjQ0RDgcJpPJEAqFWFpawuv1yopGIT1F5aLqglFrtoV0EvUmbrebK1eusLKywr1797hz5w61tbUEAoEcnVKFSEXbLhYWFpiZmWFkZIT5+XmZpFxdXY3D4cixxlXrfzfIqdbUw7q3JJPJMD8/z/379+nt7ZXbr7S3t9PQ0CC//7KQUcWmxBTumtu3b5NMJgmHw5SXl8uN2pubm8lkMty4cYP+/n4AxsfHWVxclM0IYP3BqK4e8bCTyaRUBZLJpCTq7OwsX331FbW1tbS3t9PS0sLc3NxzK3MIh8Ncv36d3t5ewuEwAwMDhMNhvve97+X4R5+HFFJbgqukXFxc5Pe//z2Dg4N4vV6ampqorq7e1UYEzwub3kE6naaoqIiOjg6++OILPv74Y9xuN6FQiPb2dmpqatB1nYMHD3Lv3j3u3r0LZDuBHTx4EFiXIEIPElt8CL9ZeXk5Xq8XQC7rJSUlUln/8MMP6erqIhaL0d7eTnt7uzx+t2AY2b6dmqaxsrJCKBTC6XTKrh8iKVgcu5s6phAOatWi8JjMzc0xOjrKxYsXOXXq1IbtcV5GPHFqmc1m/uiP/oiWlhaGh4eJRqNUVVVx5MgRuV3JW2+9RV1dHSMjIwQCAU6ePElJSUlOb0rDMGhra6OhoUFuWxwMBvmbv/kbGT5saGiguLhYErSmpobh4WFmZmZobGyU2S+7LaEymQx+v5+mpiYGBweJx+NUVVVx6NAhPB6PDN0JqKUX6lKuGkdCsm40dpXgaiIFZFeVpaUlhoaGuH//PpqmceXKFY4dO0ZHRwcej0fq98I4e9kJuikxxVLsdDppbW2ltbW14HElJSWcP3+ec+fOPVYHI2CxWOT+O4Ds6NbR0SH9nWLnXPE9v9/P6dOn5Xeel64ktqJrbm7G5/MxMDAgt2xWm0gJK1hIs/zN6TVNkzXnQt8WBqWAsKaFG8dkMsn2fiK48fvf/56bN28SjUZpbGzklVdeobW1VRqPAqpB+LLjiX7Mp4E4rpAhshGE20KVKvF4XHb9fZEQBprP5yMQCMgdzwKBQE5M2TAM2QxWzctUz5Pf8EEQ0G63S0tfeBDETsJjY2M8ePCApqYmTp8+TTAYlCHekpIS2Sspvy/l14GQAi9USxYvIpVKyfYje2EJElLM7/dTV1dHQ0MDVVVV+Hw+YD1cq2ka7e3tcj/LRCJBTU1Nzh7h+auHmlAcjUblCtPb28vVq1cZHR2luLhYXtPpdMpd18SEVc+ZTCZlKcTXCS+MmKlUipmZGW7fvk1nZ+djWyy/SAgp53K5qKmpoa2tjbq6OqnaZDJpQqEQNpuNyspKHA4Hc3NzrKysYDabqampkfH1RCKO1ZpdckUEbWBggMXFRWKxGMeOHeXEiZN4PG5aW1tpbGykurqayspKiouL5YauQg3I70m5E3kBexHPjZjqkhWNRhkdHaWrq4tIJMKlS5d2PO0q3/AQvyvUS0l1QKvlFGIXN5fLRSIR486dr0gkkni9RdjtNoq8XhwOJ2azQSoVJxwOMzKaYmxsBE3LEA6HiUQjBMoDtLS0YrGYmZubZnl5EZvNTDAYoKKiHK+3iNIyP5WVAWx2Ox53tiV4Op0bZQJyntPLEsXZCp4bMUX4LJlMMjk5yc2bNxkeHubQoUMUFxfvWmfajSB8gYlEglgsxtraGisrK6yurua0T1xYWGBlZQmb3cLDqXES8SS1tVW0tLZiMhtkMkkSiSiZTJJINMTs3BSzM7MsLi4SjUXRdR2v10t9bwN+v59QKIyuaZSWlj+SxDVYLGC1mnC5vFgsNjBA07J7YRqs661iYqkG5ouoFHgeeG7EFBbm9PQ03d3dTExMPGap77SzWnXRCFfK2toay8vLkoDhcFj6KldWVlhZWZFLp9vtlvuFezxOvMVFpD0ZTGYTsVgEXddkckoylSCdTmIyQXVNFS63U8bxs1sCrrAaWkHXQc9ozM3NsLyyzPDIMEVFHoqLi/GV+Ckp8eHz+fB6i7BYzJhNFnjBNVUvAs+FmEI6jY+Pc/PmTcbHxzGZTHi9XiorK3Mq8nZKXxKZTUIihkIhotEoMzMz9PX1MTU1lRMKLSsro66ujuPHj1NSUkJJSQk+nw+3243VasFqM2OxGKytrRGNRllYWGBubk7G1NPpNF5vMc3NzbS2tkpCiuwqXdOJxbPjWFhYZH5+jvHxCe7cuUMsFpUToby8nOamZpqamnE4PPj92dwAsUfSHwqeCzFNJhORSITu7m4GBwdJJBJyD57y8nJgPct9uwaQmATxeJz5+XkGBga4e/cuAwMDRCIRuXHSqVOnaG1tlZuhCn3N4XCwtrYmEySy50uRTmUwbGbcbjdut1tuFRMKhbIRMm8RVYEqKioqZNMAkRsgzuN0OvH7/dTW1uKwOzCZTaSSKdYia8zOzvLw4UMePnzItevX+NWvf0VkLUVHx0HOnDlDS0uLdF0Jq//rLDmfGCvPx9M+DLWk1mw243Q6OXbsGOl0mq6uLtbW1qiqqpJ7+oicyvzzq1EVcf2NljPDMGQLvVu3bnH//n1ZByRKVH2+7FJps9lIJBKk02m5v5DYdEpEtMQ5MxkrmpbCbFl/HpWVlXg8HkKhEJlMRpYLCwe62WyWW0qrkRyHw4GhZ6V5OpOWCTFFRUW0tbVJa351ZZX+/hG6u3v4+c9/zszMDMFgkEuXLnHp0iXa2tpkUs1m0ST1HbxMMBmbmML5NTNPCqupEEupiOjouk5PTw937twhHA5Lgly+fBmPx0MqlZJZO4XOlb+tijrGubk5+vr6uHfvHgMDAzgcDlpbW+ns7KS+vl66XfKzm8RLzS/sVxs5ZI/T0Y0MhpFbXqHWm6sZU0KfFZ6IjTYBVZspCHfZ+j2DCRvxeIpwOMTa2hoLCwuMj48zNTUFQEdHBydPnqShoUFmc4kxiZVD+D9fNum6q8QUmUAmk4m5uTmuXr1KOp3m8OHD1NbWAlBaWipntqjWU88hCvPFlnpCGsViMQYGBrh+/TqDg4NYLBbq6upobGykvr5e7i2U1RGtMsUun/iFpEl+RxEDHV3PJWa+JBe/E99X49aFiJ/fMeTxcZgxYQXM8vmkUimi0SihUIjFxUVmZmZYXFzEarVSX1/PoUOHaGxslEku6rlfNqNpV4ipnjKdThOLxfj9738v3UMXLlyQmz6pVXr5+qV4+YK0yWSSmZkZhoeHGR4eZnFxEbvdTnV1NXV1dVRWVlJeXi6TGoQ0VO8n/3YLScxnIaZ6nDiXGLMIU+Y/M7XyU3WU5xLdRCYN6118TBiGjrhcOp2S7q3Z2Vmmp6fJZDKUlZXR3NxMW1sblZVB7HbbS7mcb0rMJzUr3QjqKTOZDFNTU/ziF7+gqKiIS5cu5SSDiLKIQrqSml0zOjpKf38/Dx8+RNd1ioqKKC8vp66ujtraWrxerwxpZjKZnMwmMSaRfvek+8lPZSu0lAspln8uoU9uREzVWyD2WxffWf9kz5dO6xiGCQyyLiPZKZlHKkL23tbWssbTxMQEs7OzpFJpysvLOHjwIB0dHZSVlT8KkZpQb1WN+e810j5zEsfTLgeqTjgyMoLVaqW9vV2WPYiXqi75wvgQDyyVSsltiIeGhlhbW6OkpISDBw/S3t5OMBiUyQz5+xpuFHPfyGja9DiTGbNhQtdzv1soWiWkrVBh8pdyldD5CcDCXWYYOrpuoGkZ1NNnCZ49dzqjo2lmdMPA7rDQ2naAmpogM7MzTD2cYnFxkdu3bzI2NkzHwYM01Dfi95fl7Mmp+nj32lK/qcTcKsSLSafTjI2N8eGHHxIMBrlw4QLV1dU50kFIOJE4rOs68Xic1dVVxsfHuX37NrOzs1RUVHDs2DE6OzspKyt7Ypa2eo2nGWt+il6OSvGUS7m4Z/V3hQwuVZoK5IdD1ZS57PfIOtzNFsB4tCpo6Lr2aMxW7Hab1NOXl1e4e/cOAwMDFBV5qaysoaPjEM1NB/B6i+RkEM9fjHGvSM5dI6amaSwtLfHTn/6USCTC22+/zcGDB3O6buQntWqaRjQalVV+Q0NDWCwWTp8+zblz5+SOr0+TCLtXiFlItytUHpJPTFWaqseI41R1RVRA6vq6RW6xWHE4HESjUe7du8/Vq59TVlrB2bNnOXToEGVlZTmtYYQE3SuJNLvmYE+n00xOTrK0tERnZyc1NTUyU0Yk4grHszj+4cOHfPXVV9y5cwe73c7rr7/OpUuX5BZ9sH0H/PNGIV00Hxvdz2auMzVECbkTQHgyhEF1/PhxmppaufbFdX79619z//59rly5woEDB7BarY/tgLwXsCMSM/8hGYbB0tISH330EQ8fPuS73/0uVVVVctkQ7WFEIm0qleLTTz/lk08+wel0cvnyZU6ePClLMADpqAaeyv2xUxLTMIyCEhMoKDGFWpI/DhWFsvwLScz8TCjVR6r27RTkEknWiUSCSCQi8zSj0Sgej49UMs3w8AjXr18nFApx4cIFXnvtNSorK3OMz3w31osQBNsmpniYqpN4bW2Nrq4uPvzwQ958801Onz4tfYmCjOpy/1//9V/Mzc1x7tw5Tp8+TVVVFQ6H4zEXC2w9iUHc5kYVlvnLr+qqypJSA1Ou5Csk0R5zNW1gWAkDUP3kTyYRdhSkSafTJJPJnD5K6vIr/hXLvGwvqGmYTTa0THbMy8vL3Llzh56eHsrLy3nnnXdob2+X70jot0JNeBHJ2zsiMdXkVV3XGRkZkc7073znO5SWlsqHJepUlpeXuXXrFteuXcPn83HhwgWamppkuHA3UMgpXgiq9Mrem4bFAhZF8SkkCQtJ380gVo+NWoTnE0I1jJ40DmFpyz8ZFlZXwxhGtho1Ho8zMzPD1FTWgj969CgnTpzI8XSIMbwIg2hHdEyxfJnNZsLhMOPj40QiES5evIjf789eSLFOx8fH+fTTT+nr66Ozs5Pjx49TU1OT00R0LyEr4UxYLWYM1n1/W+05r5JefXb5lZeFxpGvYxcykh4/h+q2yuYteDwevF4vtbW1TE1NMTg4yODgIBcvXuTo0aN4PJ4X2lN/R4gpdMZkMsnExARTU1MEg0GZ/iVixvF4nL6+Pm7fvs3S0hJHjx7lG9/4hpSoexVZIunZpVx5TwZbe2kqMdWoV6GS4Hy1IF9iit9v9jOQUzME6x4Rv98vo0PDw8PcuHGDhYUFDh/upLa27oU1T9iRq4rZODc3x8jICKlUiiNHjsgabMMwZCuT7u5uMpkMp06dkg3pxUPaK1CXx3UXjU4mk0uI7RgGqmEjdG+hQhQiJKxLRzGJhe75pFXGZALd0LLOecNA09PrUbVUnEQiRlNTA4FAGXfv3uXWrS9ZXJznwsULtLS04nQ4MdDlpMx+d3ff17aJaRjZeHcqlWJycpKVlRWCwSD19fVSEV9ZWeGrr76S/XXOnj1Le3u7rJ+G3OrBF+0OUrOL1p3OBpget663CkEo1dMgri2scuHGUSWryFbKj62LZ6eOSx1fMhnDZNYxG2AyaVgsVsxmE4lEBkwaGS1JIODnzNmT3L9/n5mZh3z++VWSyRgd7QdxuhwYuo7JZMZsFrmgu/eetk1MMduXl5eZnp7G4XDQ0dFBIBBA0zQWFxe5evUqExMTnDhxghMnTuTskAAvtlxgI+Mh37ENJtihMWqaJlu9iPOrW1Crv8t3K6ljFMcWynLKJ22W2Lq8vq5rj6R1BrM5G0NPpZOUlfl59dVXmJycoLu7h//5nw9IJRMc6uzM+p6t1kfRp93Ftq1y0Ybv+vXr3Lt3j+bmZr7xjW9gsViYnZ3lJz/5CZFIhHfffZejR48C2aQMh8MhU9nkYJ4hrW4rKGSV58fZxTjyvgk87i7a6PzP+kgNw8jpwak+A9VIEn9TdU0Rscm/J/X3hXy6664wPUePjMfjMjdW13VpE/zJn/wpZ8+cw+l0YLM5sVi231FvM2xbYtrtdrq7u7l16xZ+v5+Ojg7sdjtDQ0P8+Mc/JpFI8M///M/U19dLB7vD4chxSbxIFLKuhaTaTSleiEwisVcYQmqCiiCn+OSPP/+e1EmYn1UlVCyx664gocjEF01vTSYThw8fxmQy8X/+z0/QMhkuXbqM01m0a89FYEvEVGOr4XCYsbExUqkUFRUVuFwurl27xq9//Wvcbjc/+tGPZGRBOJVFzY8oDYB1y/55L+liycx3sG8VhSRmIUOmUHRIXFeQTeytJD6q/i0ML7H8i7+L/+dH1/K3HRQTTyRQizGIySCuDdDS0sLbb7/Nz///n7Oyusobr3+TioqgHKtqvO0UnomYhfQaUdZQU1NDY2MjDx484JNPPsHv9/P2229TUVEhl/twOEx/fz/T09NUVlZy9OhR/H6/rOEWmxE8T3IWsqy3shzDxg78J95Tnj6bnzKXb5Wr4UpRTiE+4p7yw7aFxibSDEXiibi2KqUh25Hk8OHDRKIRenq6sVhsvHLpG1RVVUtHvqZtb0+lfDwzMWE9ZCeam46OjhKLxQiHw8RiMdmmura2Vn4nHo/z+eefs7q6SklJiWxgf/78+ZyH+ELisjt8zXy1YCOneP7xORlNj/TIfN3Q0HO3RBSEUj/imuryX2jCqC4r9drq/81ms8xCunD+Ai6ni5GREew2FxcuXJR7Oe00nnnNkv6vZJKhoSFmZ2dpb28nkUhy48YNQqshTp3MlsaKB2qz2ZicnKSvrw+bzcbhw4cpLi7h/v37jIyMSD1nL/kydwpqYsZGn40iLIIwOcnGeQbNM40l72fhetrsI9QA0Ymvra2NQHmAwcFBbty4weLiojzXTuKZJKaa5RIOh+nu7qa4uJjSUj+pVBJd13C5nMwvzFG3VoevpOSRK8LE6OgIhqFTURGgvLyMpaVF5hfmGBoa5NChg4BJJr0+f4LmvzIDUF68ycC0xSiPkFaFMow2HVGePzffgBHH5EMsq2qsW/iZ1QmguqhUmwHW9xAV5BcbhyWTCRwOB4cPH6avb4De3gfE4jEuXbxIfX0D688NMJkwbcPP+czENIxs67vZ2VmWlpbw+YoZGOyjpqaas2dPMTo6yvXrn2OxmLj86iuYzTY0LcPi4hyZTJL5+Wm67t1menqGSCRMLBYBNFKp9KOmAw4MY/OWKE8jLQo5mQvDAPJfeNbPJ3lpMsD8uDv5sWVWWVbzj8n3iz6NXpvvDjIMA4P18+VnXKneBDU4sP63dXVWLSsWe8+rESX1XtaJawY0ysr9HDt2hEwmRVfXbUCjqMiN3+9DNx4V2pksmMwWthohemZtNZPJMDs7y+3bt7FarUxOTlBaVsKpU8dpbmqmuroSTU/x2eefUF1TwbGjx9C0FLH4GlPTEywtz9Pf30s8EScSWcVT5AA0ND2FxeoEHlfSt0LMQt97HI9IadJQpaZBGt1QdUAwG+ZHL2Z9DIXIlC/tBTmeNN5CWe35xoRhGGS0DJqea+yohFSNufxsJItlPY1O7RQnJoCQqKrkFPdgsVhkUCASWcNsMXPq1HECgVLudt3F6bDy+huvP+p+Zwazgckw5TyzZ8EzGz/z8/Ncu3aN27dvEw6Hqa2t4rXXXqOpqQnd0KkMVnLx4gVmZ2d47733qKurw2634/UWcfLkSc6cOUtbaysDgwP87Gc/y3a9MOVW771oqOHR3UC+haxKKPWawpuR/11QJp2idwqICaM64VVjSfwrLGoMI2dDLwF1mVevLwIjGTI0NDZgtpj55S9/ic/n49TpU7JduW4YWLb4Xp+JzolEgvn5eSYmJh4t4z5+8IMf0NHege2Rsmyz2aisqOTs2XNMTEwwOjqK1WqlqamZjJaR2xAnU9ltVLL15aJib2s3sdMQEkIYADudkyiWzXzjJ38iiNxV8VE7eshjDSPH3STOLyJJosxCJWS++8lgPftIlECr9w+5JI1EIpLwyWSS6upq/uRP/oT/+//9X+7du0cinsZs3l73jydKTHU2i51cx8bG8Pv9/N3f/R31DfUAaJpORssq+m63h0MHD3Hu/Dk++eQTmpqaqKmp4datW3Tfvw+GQW9vL/F4HL/Pj6HvnVoTeHw5LrRsb+TaepKULeRgF+fL/znHWjeQSq7JbM4JChSS7kIi5ocs1WW6kNNe9Z2qUlVVEzRNk11N7HY7mUyGhoYGTp06xdWrVykrK6ehvhG73YnZasEwnt0lZ/mXf/mXf9noj+pMjsfj3L59m9/97nekUin+4i/+gqNHj2K1WTDQMMj1p4m2eh988AEdHR3U1dbhcrtIJBLMzc1hNps5d+4crW2tWG1ZSWAxWx/pJIVfeL5S/jS+z3zjI/d72QpIw1i3nNXoifryCkF15WyUAqdeT9UjRbMDIZELfU8lRzqzXlym592PSDIW/xf3LeLgJSUlOeqJWObVojWVyOpzEERcz4g3SCQSJBKJHI+DYRiUlZUxMTFBZG2N8vIAfn+296mu50a2ngZPlJhCPxkfH+f69essLS1x4cIFGUNNpVJYrbkEEd8JBCrwuD3MzMzQ3NzC4c7DVFdXZ31iNjv+Uv/6rr0m8yNdaQsNCTZAoe8Vkiy6kXVzPCsKnWsjSahKynxDR9UH1e+JfdsFMcT+7OpxIqaukk64eETdj1rIpxJOtF1Ux5bvjBfEUw04MQnF9opCWJSWltLe3k5PTw9F3ju43EVUBIIYhi5zbp9Wcj6V8ROLxejv75cbQZ05cwan0/noYo97q7IPB9wuF42NjUxNTRGLRqmsrMDtdqEpkmjdV/hU41XOv/WSBuU3ZK3yZz4VsLXQpSqxNjtX9pg0hgGalnmkL+bnYGZJG4/Hc76rVlkaRnZ3DEFy9fzqdTdeFZCri7CwbbYsbcREERNA13Xq6+sZHx+n98EDir1+zp4twu12ywnxtKUzT2wRYzabmZycZHx8nLKyMi5evEhtba2ccRaLASYdVeJkH54Jq8VOY1MTPQ96sk3y9XJ0A3RNR9N1LGYzFrMFi9mCyWTGZLKQZcnT90ZSx7oVZO/RkjP+Qq/o8US4R+UWOUcLPezxb5pMWb+oxQJms17QFfS4H3OdkJqWAUyyj+f6MZrc+VicRxgyIqE4FothGBs3LRPky/XDmh7dmxkDDQydrK1sPEoytsi9ilSpKvJx79y+y4MHPQQClXR2dj5zo9knNm4NhULcuHGD2dlZDh06RH19PbFYDOCR4pvCQEnD0rOkM2HGanXgcLhYXQkxMzOLy+V+tGQrDnBEaYBI188l5kbLo7p0wXpMNz8trFCMONdBrWcd6CrBTLkuHbPZDMbjGUGpdCpruKn3k/fwhYoiljOxjFqsj4wXw0DXDbJdNB6/T6n7KQkaFosF86N2MSaykiv1qKRX3RU426fIIBaNk0pl5N/S6cwjois+UEwYZP8GBmazBbM5W2WZldzrDb+sVgtWiwWT2YzZZMVkMUinUkSjcZLJNCUlfsrLAwwPj/Hll19SVVVFIBB4ptVlU2Lqus7AwACff/45uq6zurrKzZs3ZWuSrJ6RItv8KWs2CheE1ZrtlDszO0NoNcq1L75kaHAUq9WGxZJ1VqtWYfZ9Pi4tH19+ydn6TiQ6OJ1OgsEgq6urrK6uSqmi+gLN5myFoKr8Z5e93OZVVquFdDrzSBLxqHGA+dF9i2djkEol0XQdszJRUuk0IlMcwGa1YbXaMJlzo1mWRzHojJZBy2gkkkkyar242USxtxiL1QqPCJHVNTNSMjnsDhwOB/FEnPn5BQxDp6TE96hlY7bddrYZrvVRax5dLr355RuZTAan0ykno9VqeyTVDRKJpBw3JrA/cinpuuor1R51Z86WbESjMVZWVrl37x4tLS1cvnz5saTkzbDpURaLhaqqKjo7O+nv7+fmzZtEIhFJTMMwsNnsys5cxqPlKkuArDVoxel0MTAwSH//QNY/ZrFitqy7JOTLMD1enmqxWGRvHgGRJqdGP/x+PzU1NYRCIbk5lN1uzyG12Zzd/VeQXbSqyU8gyeaNZkn/yJGC0+nE7V5PkM0uoRkyj150ofrw7IQxcLksWBCrQtbtmNF1NM1A18AwTLicbsyuAj2OUuuZ64lEkrW1Nbn3pnB2u91u0unsBF1biwBIvTM76c3Y7TZ5X1kLm0dVBFqO+8fQDdKZtGyukEqlSCQSOeMSz9Rms+Nw2LFYrFgsuVExq9VKcXGJ3JVkXWA9HTE3La2IRqM4HA6SyaQMR+W3TVZdFPnId++I458VhUKShaA2TX2WRqVPO6Zc/QxyEj22eP6ciZm/WhTQdlULWhCkkP6mnlcYQhu5s1RPwWPtcTa5v6d5bsJ1KGLy6qasm35vM2KKZTA/X1IdkBpjVQeTTwzR1kT1uT2tzvEkHVMszUKHEop4oQcn/HFqZs3jRsc6scVLK+SHK1SjU8hRnv87QQLV/1loHBvdt/j/Rl6BQu9IjXurz0ZNSlYrMdVzbPaexPMp9LxV1UW1BZ4GT1zKxck2mh3iJRf6vXpj4iU/rfTLP9dmP6tj3Ewy5y+zhcaz0bGFVoZ8Czd/dSh0LvXY/Mm82Rjyx7LRtQp9N3+FUye2eg71/vK/o0KdEE+6h/xxPy02lZgq47eLjW5gp5bC/BvfSCKr97TReVXpop77acbxNATLfxZPQ658POmd5F8jP0VOPe5Z3+9GpNzq8ymEXWncuo99bBdfv1qGfXwtsE/MfexJ7BNzYZUjBgAAADFJREFUH3sS+8Tcx57EPjH3sSexT8x97EnsE3MfexL7xNzHnsQ+MfexJ7FPzH3sSfw/eJU5ZRPPxkIAAAAASUVORK5CYII=)
physics-General
physics-
A spherical hollow is made in a lead sphere of radius
such that its surface touches the outside surface of lead sphere and passes through the centre. What is the shift in the centre of lead sphere as a result of this hollowing?
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)
A spherical hollow is made in a lead sphere of radius
such that its surface touches the outside surface of lead sphere and passes through the centre. What is the shift in the centre of lead sphere as a result of this hollowing?
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)
physics-General
chemistry-
On heating a mixture of
ans
, we get –
On heating a mixture of
ans
, we get –
chemistry-General
physics-
Three identical blocks
and
are placed on horizontal frictionless surface. The blocks
and
are at rest. But
is approaching towards
with a speed 10
. The coefficient of restitution for all collisions is 0.5. The speed of the block
just after collision is
![](data:image/png;base64,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)
Three identical blocks
and
are placed on horizontal frictionless surface. The blocks
and
are at rest. But
is approaching towards
with a speed 10
. The coefficient of restitution for all collisions is 0.5. The speed of the block
just after collision is
![](data:image/png;base64,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)
physics-General
physics-
Two identical masses
and
are hanging stationary by a light pulley (shown in the figure). A shell
moving upwards with velocity
collides with the block
and gets stick to it. Then
![](data:image/png;base64,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)
Two identical masses
and
are hanging stationary by a light pulley (shown in the figure). A shell
moving upwards with velocity
collides with the block
and gets stick to it. Then
![](data:image/png;base64,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)
physics-General
physics-
In the given figure four identical spheres of equal mass are suspended by wires of equal length
, so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and all collisions are elastic, the velocity of sphere 4 just after collision is
In the given figure four identical spheres of equal mass are suspended by wires of equal length
, so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and all collisions are elastic, the velocity of sphere 4 just after collision is
physics-General
physics-
Two negatively charges particles having charges
and
and masses
and
respectively are projected one after another into a region with equal initial velocity. The electric field
is along the
-axis, while the direction of projection makes an angle a with the
-axis. If the ranges of the two particles along the
-axis are equal then one can conclude that
![](data:image/png;base64,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)
Two negatively charges particles having charges
and
and masses
and
respectively are projected one after another into a region with equal initial velocity. The electric field
is along the
-axis, while the direction of projection makes an angle a with the
-axis. If the ranges of the two particles along the
-axis are equal then one can conclude that
![](data:image/png;base64,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)
physics-General
physics-
Two blocks
and
(
) are connected with a spring of force constant
and are inclined at a angel
with horizontal. If the system is released from rest, which one of the following statements is/are correct?
![](data:image/png;base64,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)
Two blocks
and
(
) are connected with a spring of force constant
and are inclined at a angel
with horizontal. If the system is released from rest, which one of the following statements is/are correct?
![](data:image/png;base64,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)
physics-General
physics-
In the given figure, two bodies of mass
and
are connected by massless spring of force constant
and are placed on a smooth surface (shown in figure), then
![](data:image/png;base64,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)
In the given figure, two bodies of mass
and
are connected by massless spring of force constant
and are placed on a smooth surface (shown in figure), then
![](data:image/png;base64,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)
physics-General
chemistry-
Which of the following noble gas was reacted with
by Bartlett to prepare the first noble gas compounds -
Which of the following noble gas was reacted with
by Bartlett to prepare the first noble gas compounds -
chemistry-General
physics-
A set of
identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is
. The block at one end is given a speed
towards the next one at time
. All collision are completely elastic. Then
![](data:image/png;base64,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)
A set of
identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is
. The block at one end is given a speed
towards the next one at time
. All collision are completely elastic. Then
![](data:image/png;base64,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)
physics-General
physics-
The blocks
and
, each of mass
, are connected by massless spring of natural length
and spring constant
. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block
, also of mass
, moves on the floor with a speed
along the line joining
and
, and collides with
. Then
![](data:image/png;base64,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)
The blocks
and
, each of mass
, are connected by massless spring of natural length
and spring constant
. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block
, also of mass
, moves on the floor with a speed
along the line joining
and
, and collides with
. Then
![](data:image/png;base64,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)
physics-General