Maths-
General
Easy
Question
Normals
are drawn to parabola
from the pointA (h, 0) If triangle
(
being the origin) is equilateral, then possible value of h’ is
- 26
- 24
- 28
- 22
The correct answer is: 28
Related Questions to study
maths-
Given: A circle,
and a parabola, ![y to the power of 2 end exponent equals 4 square root of 5 x](data:image/png;base64,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)
Statement‐I:: An equation of a common tangent to these curves is ![y equals x plus square root of 5.](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFUAAAATCAYAAADh9EErAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAfRJREFUeNpjYBgFPED8nwI8CrCACCDePxoM1AXbgThlNBioB0SA+D2UHgVUAhlAvB6L+GgZSgEAlaUhOAJ1xAFqeFoBiF8DMQetAnUuEIdjES8A4lYqB0gyEHdgEW+GytErUCuAeDYNzWeIB+IuNDEuIL4FxMIkljnElD3ngFgciZ8IxFPonFLPA7EHLQPVC4hXoYnVA3EtjbIvyDN9ULYLEO+lYfbnwSKmA8TPgZgFj/m/gPgTEG8D4iIc5uAFoNR4BYkvCsR3cZQ31AK7gdgeiC/gyA2U5gwVIJ4PlbNBk2sH4n4i3AgKdGNo4roBxBqkevIbErsPWp5S05PYymtQatCjUUVVAw1UUDv0FJrcfSA2IdFONyA+SKpDDwOxEhSDUikTDVOpNRCvgUZeJI1r/ywg/odUhlsA8W08WR8f+EGqhoVA7AfES4E4loYBCoq0TdCKEFROnSEi+1NakYBy4TIoezIQN5Dhbh1oYiMJFECbVpdoGKCi0IIfORB9gHgxjQN1DhB/h6bO10SUjeuA2BKaW5mgFSsoQIOIKBJRQABU0I9GAcoGdaw0FrnleJo31AACQPwXiNcC8XEi1IdCm5N/gPgdtGVkSmRligL8iLRwqILDUE8X0NPSbdAkP1yBKTRQZehlIagQ3jICxgxC6GEJAFQEkvMdEPeBAAAAinRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT55PC9taT48bW8+PTwvbW8+PG1pPng8L21pPjxtbz4rPC9tbz48bXNxcnQ+PG1uPjU8L21uPjwvbXNxcnQ+PG1vPi48L21vPjwvbWF0aD5Hg4oLAAAAAElFTkSuQmCC)
Statement‐II:: If the line,
is their common tangent, then
satisfies ![m to the power of 4 end exponent minus 3 m to the power of 2 end exponent plus 2 equals 0.](data:image/png;base64,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)
Given: A circle,
and a parabola, ![y to the power of 2 end exponent equals 4 square root of 5 x](data:image/png;base64,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)
Statement‐I:: An equation of a common tangent to these curves is ![y equals x plus square root of 5.](data:image/png;base64,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)
Statement‐II:: If the line,
is their common tangent, then
satisfies ![m to the power of 4 end exponent minus 3 m to the power of 2 end exponent plus 2 equals 0.](data:image/png;base64,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)
maths-General
maths-
In any equilateral
, three circles of radii one are touching to the sides given as in the figure then area of the
is
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)
In any equilateral
, three circles of radii one are touching to the sides given as in the figure then area of the
is
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)
maths-General
maths-
If the sides a, b, c of a triangle are such that a : b : c : : 1 :
: 2, then the A : B : C is -
If the sides a, b, c of a triangle are such that a : b : c : : 1 :
: 2, then the A : B : C is -
maths-General
physics-
A block placed on a rough inclined plane of inclination (
=30°) can just be pushed upwards by applying a force "F" as shown. If the angle of inclination of the inclined plane is increased to (
= 60°), the same block can just be prevented from sliding down by application of a force of same magnitude. The coefficient of friction between the block and the inclined plane is
![](data:image/png;base64,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)
A block placed on a rough inclined plane of inclination (
=30°) can just be pushed upwards by applying a force "F" as shown. If the angle of inclination of the inclined plane is increased to (
= 60°), the same block can just be prevented from sliding down by application of a force of same magnitude. The coefficient of friction between the block and the inclined plane is
![](data:image/png;base64,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)
physics-General
physics-
The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will
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AQoL+/n4sXL3L8+HG2bdtGfX09er2ekpISHn/8cebOnUtCQsIolyMQCNDb20tTUxPvvPMOBw4cIDU1lZUrV7Jy5UqSk5OlCMrnIIrF/uCDDzh06BB5eXm3ZandkWzClJQU8vLyKC8vF5LBjh8/TnV1NU1NTUQiEcxms5CzolAoMBgMZGRkUFxcTEZGBq2trezevZvGxkZUKhVJSUnExsZKPvj/QxRhP//889TU1HDfffdFTVTkehjJpbFYLBQUFFBYWMiUKVPQ6XScOHFCKLwTDAYxGo2CEVAqlSQkJDB16lSmTJmCRqPh0KFD1NbW0tHRgU6nw2w2o9FoJvgd3jyIIux3332Xnp4eVqxYgc1mG+/mbglkMhlGo5Hc3FxKS0vJzc0lHA7T0tLCgQMHOHfuHJFIBKPRKFhwlUpFeno6JSUlZGRk0N/fz/79+zl69Chutxuz2XzNC5ajFVGE3dnZSVJSEvfcc0/UV426HmJiYsjKyqK8vJycnBxcLhdHjhxh//792O12lEolJpNJsMhxcXFMnTqVoqIidDodbW1t7N+/n46ODvR6PWaz+bYcy3wWUYRts9koKysbVfdDYiyxsbFkZ2czc+ZMsrOz6ejoYO/evdTW1gqFhsxms1ByIiEhgWnTplFQUCBY77q6OiH3/GqLKW4XRBF2ZWUlx44dIycnR0rX/ArExsaSk5PD3LlzsVgsQmXX5uZmEhIShHWecrkchUJBeno606dPx2QyUV9fz8cff8zly5dJTU0lPj7+ttz4SRRhP/fcc+zcuZP77rtP8rG/IjKZDJ1OR1FREQsWLCASiVBdXc2HH36I1+vFZrMJCVMj55aUlFBWVkZnZydVVVXU1tYK5SS+aDV/NCKKsDdt2oTD4WDFihW3dVTkepDL5ZhMJubNm8fcuXM5efIkW7dupaamBrPZjNVqJSYmRrDeqamp3HnnnRgMBj766CO2bNkiLIW7nUpFiCLsU6dOYTAYuPfeez93WZfEFzMi2sceewyj0cjevXt5//33cTqdQvm2EZdDq9VSXFxMSUkJVVVVvPXWW8hkMoqKim6fmHdEJMLhsFhN3RacOXMmsmrVqojBYIjccccdkYqKiojX6x11TjAYjLS3t0cWL14cUSgUkYceeihy+vTpSCgUmqBei4coFvs3v/kNFRUV5OXlRXWuiJiYTCYWLVqExWKhtraWDz/8kMHBQfLz8zEYDMCnbozRaOSBBx4gHA5TUVHBrl27yMnJISUlJaojVKII++WXX6ahoWFMzRGJ60cmk6HRaJg6dSozZ86kp6eHLVu20NLSQnp6Ounp6cJ5I9tjZ2dns3v3brZs2UJcXByZmZlRu+GqNPN4CzMyRW+1Wpk+fToKhYLq6mo++eQTYmJiKCgoEFYtxcTEMGnSJKZNm8bRo0fZuXOn4J9PVOWA8UQUYXu9XnJycpgzZ85tmQQ13ozMTE6ZMoXk5ORRwi0tLRVmITUaDcnJyUybNk1Ioe3s7CQzMzPq7qSiCNtsNjN58mSp1O44IpfL0ev1QqH7zs5Otm/fTm9vL+Xl5cTFxQnF8ZOSkpgyZQp2u52amhra29tJSUkhNTU1aiImogj797//Pfv27aOwsFDKFRlnRup9T548mb6+PrZu3UpXVxdTp04dVeXWYrGQk5PD8PAwtbW1tLa2YrVaycjIiApxi5a2Wltby5IlSyQfWwRUKhUWi4X8/HycTicVFRV0d3czadIkYYpdJpORmJjIpEmTCAaDHDx4kJaWFjIyMqJC3KIIu6KiAofDwcMPPxx1vtzNikKhID4+npKSEoaHh9m0aRMdHR2kpaWNqj5lNpuZNGkSALW1tTQ1NZGTk3PLuyWiCLuvr4/U1FTmzp0rxFglxh+5XI7BYGDmzJl4vV4++ugjzpw5g81mw2KxCGmwBoOBzMxMIpEI+/bt4/jx4xQUFHxh+eibHVGEnZ6eTmlpKRaLRVqjJzIymYy4uDjmzJlDOBymqqqK5uZmUlJShDwT+FTc2dnZhEIhqqqqaGtro7S0dMw6zFsFUYS9fv16du3aRVFRkTR4nCBUKhV33HEHsbGxwprJkUjISOafXq8X9u3ZunUr7e3tzJo165ZcFS+KsF944QUOHTokDR4nGLlczrRp0zAajcJmVykpKaSnpws+90iqrNPp5P3336e/v59p06ah1WpvKXGL4heMbCt9K30w0YpMJuPJJ5/E5/Px/PPPC1scLliwQBB3YmIi//RP/8TAwAC///3vMRqN/M3f/A02m+2W+Q5Fsdgej4dJkyYJtzWJiUUmk1FaWoparWbHjh3C6qbPhvliYmJYuHAhx44d4w9/+IOwzvKWyS0RI4UwEAhE/H6/lLp6k+HxeCIvvvhiJCcnJ/LAAw9EWlpaRh0Ph8OR/v7+yP333x+Jj4+PvPLKK5H+/v4J6u21IYrFXrt2LevXr6e8vJyEhITxbk7iK6JUKsnNzSUSifDRRx/R3t7O7NmzhQH+SPLU7NmzqampobKykpycHLKysm761AhRHKbOzk7Onj2L1+sVozmJa8BsNvP000/z1FNPcejQIX72s5/R398vHJfJZGRlZfHLX/4Sg8HAv/3bv1FTU3PVzbZuJkQR9kgd6Mj4lwmUuEZkMhnJycmsXr2a5cuXU1lZyW9+8xt8Pp9wjkKhYObMmfzwhz/E6/Xy4osvcuTIkQns9Zcjiiui0+mYMWMGZWVlxMXFjXdzEtfISGZgWloaFy5cYMeOHcTFxY2qy61SqUhNTcXtdnPgwAEGBgbIy8u7aV1LUYQdDoeFDUxvtzIAtwoKhQKTyURqaipNTU3s3buX7OxscnJyBHHHxsaSkZHBhQsX2L9/P0qlkqlTp17zXvZiINrM4969eykrK5PWPN7EqFQq4uPjSUxMZO/evdTX1zNr1izi4+OF+LXRaCQpKYmWlhaOHDlCUlIS+fn5N11RHlF87IaGBvbt28fg4KAYzUl8DfR6PQsWLOB73/sera2t/Nd//Rd2u13Yq14mk1FeXs7q1atRKBT87ne/o6GhYYJ7PRZRhG00GklISLjpQ0QSn2IwGPjmN7/JypUr2bBhAxUVFbhcLuG4Wq1m/vz5PProo3R1dfHqq6/S2dk5gT0eiyiuiN/vJycnh/Lycql23y3AZ1fA79mzh9raWqZNm4bNZhOyM+Pi4rBYLHR3d/PJJ5+g1+spLS29abI3RRH2SL6vtL3yrcNITZKkpCQ2bdpEZ2cn5eXlo/ztkXrcBw8e5NChQ8yaNeuqu6JNBKII+9e//jUVFRVMnz49Kpf6RytyuZyCggK6urrYvHkz8fHx5OfnC/kiI6WMdTodO3bs4OLFi9x33303xc4KovjYZ86c4dixYwwPD4vRnMQNRCaTsXbtWgoLC1m/fj2HDx8eNXmj1Wq58847uf/++9m3bx8bNmwQBpoTiSjCVqlUqNXqWyblUWI0FouFH/3oRygUCtatW8fx48dHzSJnZGTw3e9+F4vFwq9+9Ss6OzsnfJZZFFckMTGROXPmCNU+JW49srOz6evrY/v27cTFxVFUVDTKJdHr9dhsNt5++20GBgZYsmTJhMa2RRF2bGwsSUlJo0rdStxayGQypk6dytGjR6muriYtLY3CwsJRU+5ms5menh7ef/995s+fj81mm7DvWxTf4LnnnuOZZ57h7NmzYjQnMU5YLBaeffZZTCYT7733Ho2NjcIxmUyGxWLh+9//PgaDgZ///OcMDQ1NWF9FEfaVK1fo6uoaNeiQuPWQy+XMnTuXJUuWcPr0aT788MNRKa4qlYrc3Fx+8IMfcODAAbZs2TJh4hZt8KjRaKTBYxSg0+lYtWoVxcXF7Nixg6qqqlHHY2Njefzxx5k1axbr1q2jq6trQqIkovjYycnJzJs3j6lTp972+w9GAwaDAYVCweHDh+nt7WXGjBlCcttIHZOkpCT+8Ic/YDAYmDJliujpyqKYUK1Wi9FolCx2lKBWq5k3bx7z58+ntbWVnTt3jrLKcrmcu+++m/nz57Nx40ba29sJBAKi9lEUpb377rv893//N1euXBGjOQkRsFqtLF26FKvVyqZNmzh37tyo43FxcXzve9/D6XSyadMment7Re2fqDOPn80Qk7i1kclkFBcXs2zZMmGbkFAoNOqcWbNmcd9997F7926am5tFDR6IIuzk5GQyMjIk/zrKMJlM3HPPPRQUFPDBBx9w/vz5UcdVKhWrV68mEomwbds2UVNbRVvzWFZWRl5enjTzGGUYDAbUajWVlZXI5XLmzJkzaixltVrp6Ohg3759ZGRkMHnyZFFSW0Wx2BkZGeTm5kqijkJiYmIoKSlh+vTpvPvuu1y8eHHUcblczsqVK1GpVFRWVo45Pl6IIuyf/OQnfPvb36a9vV2M5iREJj09nSeffBK3280bb7wxJm5dUlLCzJkzqauro6amRpQIiSjC9ng8uFyuMYMLiehArVaTn5/PggULePPNN+nu7h6V3adQKHjwwQfRarXs2rVLlNQK0QLLMpnsliwgLvHVsNlsrFmzBrfbzYsvvjimUtTcuXMpLy/nwIED7Nq1a9zTWkUR9r/+67/yzjvvMHnyZDGak5gAlEolGRkZLFmyhNdee41Lly6Nckk0Gg2LFi0iPj6e6upqTp8+Pa79EUXYg4OD2O120WefJMTFbDazevVqhoaGeOmll0atmJLJZMydO1fYGbi6unpc+yKKsF999VV+/vOf09XVJUZzEhOEWq2mqKiIu+66i7fffptz586NMmaJiYnMmzcPlUpFdXU1ly9fHre+SGmrEjcMmUyGwWDgO9/5Dv39/bz22mujiiQpFArmzp1LWVkZzc3N1NbWjltfRBF2SkoKWVlZ0szjbYBarWbBggVMmTKFLVu20NHRMWogmZGRwbx58/B4PGzdunXcFniLMvNotVqZOXMmubm5N8XSfInxY6TYzvDwMDt27MBisVBUVCSkrSqVSmQyGceOHePMmTNMnz6d9PT0G94PUSy20+nE4XDc9MXCJW4MCoWCRx99lJSUFDZv3kxnZ+eoCElubi7z58/HbrezdevWcVmIIIqwN2zYwCuvvCJ66qLExCCTycjOzmbp0qVcuHCB2tpanE6ncNxkMlFeXk5iYiLV1dXjkhwlirB7e3vp7OyUBo+3GU888QQmk4mNGzfS0dEx6lhubi533XUXnZ2d4xL6E0XYWVlZ5OfnS7sZ3GZMnz6dGTNmcOLECVpbW/F4PMIxm83GvffeSyQSYePGjTd8fyJRhL169WrWrl0r7cp7m6FQKHjssceEzL7PuhxqtZrc3FwKCwtpaGjgxIkTN7RtUYQdDAalWcfblHvvvZesrCxqa2tpbW0dlQiXkpLCsmXLcLlcVFRU3NB2RRH2L3/5S5599lmpYM5tiMlkYtmyZTidTurq6hgYGBh1bM6cORiNRrZs2XJDx2BSdp/EuLN06VIyMzPZu3fvGJcjISGBu+66i46ODg4dOnTDQn+ilV/Q6/VS3b7blLy8PKZNm8bZs2c5evToKHckISGBZcuW4fV62bhx4w3L2RdF2C+88AIbN24kLy9PjOYkbjLkcjmLFi0iKSmJw4cPj1pJFRsbS3FxMRkZGWzevBmfz3dDcrVF2TCksrKSw4cPEwgEvtQd0Wq1fPe73yUrK0tyXaKIWbNmkZeXx9GjR2lsbBSMnEwmw2Qy8Y1vfIPXXnuN/fv3M3/+/K+9H6howq6srESj0XxuhyORCKFQiJiYGB566CEyMzMlYUcRCQkJ3HHHHTQ0NFBXV8fSpUsxGAzAp1vwPfjgg6xbt47NmzczZ86cW0PYTqcTjUbDP/zDPzBp0qSrnjM0NMTOnTvZsGEDfr9fjG5JiIhCoeDOO+9k+/btHD16lLa2NmbNmgV8urqmsLCQnJwcPv74YzweD3q9/msZNlGEXVhYKGyMmZ2dfdVz+vv7OX36tJQoFcXk5+dTUlLCli1bqK2tZebMmUK0TK/XM3/+fH73u9/R1taGyWT6Wpmgogwev/0Ukj0AAAkySURBVPnNb/L973+fpKQkMZqTuEkxGo1Mnz4djUZDfX39qFqOGo2G+++/n1AoRHV1NW63+2u1JYqwT506RVNT09furMStT2lpKQUFBZw8eZIjR47Q09NDW1sbbW1t6HQ69Ho91dXVX7vOoyiuyNtvv82JEycoKSkhNjaW/v5+fD4fGo0Gk8mEUqnkwoULwn9wIBDA6/XS09NDKBRCoVBgs9kIhUIMDAwI15rNZpRKpbBLlUwmIz09nWAwSG9vL8FgEJVKRWJiIpFIhP7+fvx+PzExMSQmJhIMBunp6QE+9QEzMjIYGhoScsfj4uKIj4/H5/PR19dHJBJBo9FgtVrx+XzCmj21Wk1KSgpDQ0MMDg4SDAbRarWYzWb8fr+QrjtyntvtFp6LiYkhKSkJl8vF4OAgoVAIrVaLyWQiEAgI5ymVSrKysnA4HPT39xMOh4mLiyMxMXHMtWazmUAgIPRPpVKRmZnJwMAADodDOC8+Ph63201/fz+RSITY2FgSExPx+Xyj+pyWlsbAwABOp5NQKIROp8NsNuN2u7Hb7cL7sNlsDA8PC99jbGwsVquVwcFB3G43MpkMo9FISUkJ9fX1rF+/nqysLOE78Pv9yGQympqaaG9vJykp6brdEVGE7fP5GBgYIBAIcPbsWd59910uXbpESkoKK1euRK/X8z//8z80NDQQiURwuVx0dXXxwgsv4HK50Ov1/MVf/AXDw8N8+OGHdHZ2kpqayuOPP47RaOTXv/41fr8flUrFT3/6UwYGBli/fj0DAwNYLBZWr16N1+vlww8/pLu7m0mTJvH0009jt9t5+eWXhbV6v/jFL6ivr2fr1q04HA7y8/NZtWoV586d47333sPn85Gens6zzz7L+fPn+e1vfwtAamoqf/d3f0ddXR07duzA4XBQWFjIY489RkdHB+vXrwc+XUn0j//4jzQ3N/Pmm28SCoXIzs7mT//0T6mrq6OqqorBwUGKiop4+OGH6e7u5tVXXxUE8cILL3Do0CEqKirwer3k5+fzrW99i4aGBiorK3G5XBQVFfHoo48K7crlchITE/nVr37FgQMH+Oijj3C5XBQWFvLEE0/Q2NjI1q1b8fv95Ofns3r1ak6ePMmbb76JTCYjNTWVH/3oR+zbt4/du3czNDREWVkZjzzyCC0tLbz33nvApxmcf/3Xf019fT1//OMfgU996meffZa9e/dy8OBBwuGwsImtTCZj+/btpKSkCLs2X7lyBY1Gw5UrV9i2bRsFBQXXnTgnirAzMzNxOBzExsYyMDDA2bNnOXPmDF6vF6fTiVwu58KFCwCUlZWh1+vxeDycPHmSwcFBTCYTLpeLoaEh2tvbOXv2rHCtWq2mtbUVn8+HWq3G5/MxNDTE6dOn6e3tFSypx+Ohvb2d8+fPI5PJ8Hg8DA4OcuLECWQyGWazmWAwiN1u59SpU/T19RETEyNYtNbWVrxer3A3GbkWPq105ff76evrE64deQ8Oh0M4b2hoiEAgwMDAAK2trcJA2efzceXKFU6ePEl/fz8GgwG32z3q2pG7jt1up62tDbfbjUajGXXt4ODgmHblcjnJycmEw2H6+vpoa2vD6XQK54085/V60Wg0eL1e+vv7hc/F5/MRCoXo7e3l5MmTOBwOEhIS8Hq99PX1Cf2LRCIEAgHsdrvwnEajIRAI0N3dTUNDg7BfzeTJk7HZbHg8HmbPns3ixYtJTk6mp6eHt956i7q6OuHuer3IIiLsNDlSUyQ+Pp5wOMzQ0BDBYBClUolOp0Mul+NwOAiHw8jlcsxmMwADAwPCcyaTiXA4jMvlGnWtQqEQbofw6c5WwWBQuG0qFAoMBoNwJxhxTwwGA6FQCIfDAXw6O2axWIRybOFwGLVajV6vJxAICCtAVCoVRqORYDAoXKtUKjGbzXi9XoaHhwmHw2g0GnQ6HcFgUFiprVQqBddm5LmR1/N6vbjd7s+9Vi6XY7VacblcuFwuIpEIarUag8HwpdcqFAosFgsul2vUeXq9Hp/PN+b1/H6/8H6VSiUJCQkMDw8L18bExKDVavH7/cLmSSPb4Y0YHPjUjTGZTIJ753a70Wq1eDwe3nnnHd555x2GhoaQyWRYrVY6OzuFPdyfe+45lixZgl6vvy7NiSJsCYn/j8/n48KFCxw5coTz58/j8/mEscDs2bPJzMxEpVJd9+tLwpaYcEYy+j6bAToSDLhepN2OJCYUv99PR0cHx48fHxXiGx4e/lqTdaIMHiUkPovdbmf37t3s2rULpVJJdnY2g4ODnDp1CrPZTEZGBhcuXGDt2rXk5uZeVxuSsCVEpaGhgZdffpmLFy/yzDPPMH/+fFQqFeFwGK/XS3NzMz/84Q9xu9382Z/92XW3I7kiEqLR2NjIf/zHf3D06FGWL1/OkiVLSEpKwmw2k5CQQGpqKnfffTdr1qwB+FquiCRsCVHweDx88MEHVFVVkZ+fz4MPPojRaBxznlar5cknnyQ3NxelUnndiw4kYUuIQnNzM5988gk+n4+CggLS0tI+91ybzcZTTz2FXq+/7jWQko8tIQr19fVcvHgRm832pVviyWQyFi1ahF6vv+5tyiWLLTHuhMNhjh8/jt1ux2azfaG1HiE5ORmdTnfdsWxJ2BLjTigU4tKlSwwPD6PVakXZ71MStoQoRCKRcd8p7LNIwpYYd5RKJXq9HpVKhdfrFaXqriRsiXFHJpORlpaGXq+nr69PlDrpkrAlRGH+/PlkZmbS29vL+fPnv3Tyxefz4Xa7r7sylCRsCVGYOXMmpaWlOJ1ODh8+TEdHx+f63KFQiMbGRnbs2CEsTrhWJGFLiEJiYiJr1qxh9uzZVFZWsm7dOtxu9xhxRyIRWlpa+O1vf8vkyZNJSEi4rvakfGwJ0RixxM8//zy7du1i6tSpPP3009x9991otVq6urrYv38//f39fOc73yEjI+MLJ3K+CEnYEqISCATo6uqiqqqKqqoqrly5IqzqLysr46677mLGjBmYzeavVZ1XEraE6IRCIdxuN4ODg/h8PmFd60i56bi4uK9dt1EStkRUIg0eJaISSdgSUYkkbImoRBK2RFQiCVsiKpGELRGVSMKWiEokYUtEJZKwJaISSdgSUYkkbImoRBK2RFQiCVsiKpGELRGV/C/K3wL+0BMg2wAAAABJRU5ErkJggg==)
The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALYAAACmCAYAAAB3JnWfAAAgAElEQVR4nO2deVRUV57HP7UDtQNFFTsIAsruFjVm0TYuiSbGLKaTtH3szvRk1p6l25mec7qnJ71Nz0wmPZPlzLFj0kmnO5sJ7lEkKgZFBUFABRfckEWkoCiK2pf5I8M7YTCLRh5avs85dYB679W9VfXl9373d3/3d2WRSCSChESUIZ/oDkhIjAeSsCWiEknYElGJJGyJqEQStkRUIglbIiqRhC0RlUjClohKJGFLRCWSsCWiEknYElGJJGyJqEQStkRUIglbIiqRhC0RlUjClohKJGFLRCWSsCWiEknYElGJcqI7cDNy5coVqquree+992hra0OpVGK1WklNTSUSidDf309MTAwzZ87kkUceIS0tDYVCMdHdlvgMkrCvgslkYsGCBdjtdpqamggEAqxYsYL77ruPSCTC0NAQu3fvZt26dbzxxhv84Ac/YMWKFej1+onuusT/IQn7KqhUKuLj45k0aRImkwmfz4fNZmPSpEkAhEIhkpKSkMvlrF27ln/5l38hPj6ee++9F61WO8G9lwDJx/5CVCrVVV0MhUKBzWbj8ccfx2w2c/bsWT766CMGBwcnoJcSV0MS9nUil8sxm80oFApkMhl2u51AIDDR3ZL4P65Z2JFIhE8++YSenp7x6M8tQygUoqenh6GhIQDKysrQ6XQT3CuJEa5Z2J2dnbz00kscOXIEr9c7Hn266fD5fPT393PlyhUuX77M+fPnaWxs5PXXXwfg3nvvZfny5RiNxgnuqcQI1zx4rKqq4uDBg9hsNoqKisjMzByPft1UDA8Pc/ToUcxmM8FgkI6ODhobG9m2bRvJyck8++yzpKeno1RKY/GbhWuy2ENDQ1RUVGC329mzZw+nTp0iHA6PV99uGhQKBQkJCeh0OnQ6HRaLhYSEBDIyMlCr1dTU1NDW1obH45norkr8H9dkYg4dOoTD4SAmJoYzZ87Q2NjIrFmzov4WbDQaKS0tZeHChcJzjz/+OHV1dfz5n/85r7zyCseOHePFF1+koKAAuVwak080X/kbCAaD/PGPf+TBBx/k4YcfRqfTCVb7y/D7/QwODtLb28vly5fp7e3lypUr9PX1Ybfb6e/vx+FwMDQ0hNvtxuv1EggEbuq7gVqtZvbs2axduxatVsuePXtobm6+bcYdNztfyWJHIhHOnTtHY2Mjf/u3f8vcuXNpamqioaGBxsZGpk2b9rlTyuFwmCNHjrBr1y6OHz9OMBhEo9GgUqlQqVSo1WpiYmIwmUzEx8cTHx+P2WwmPj6ehIQEDAYDSqUSuVyOTCYb9fNqDzGRy+XMmDEDlUpFJBLh1KlTuFwu4uLiRO2HxFi+krCDwSCvv/46S5cuxWazER8fT3FxMcePH+fQoUMsXrz4qoPISCRCZ2cnTz31FJ2dnQQCAfR6PRqNhlAoRCAQwO/3EwwGx1wndFCpxGw2k5CQIDwsFgtWq5Xk5GThYbPZsNlsqFQqAGQy2VV/XgtfVjo8HA7T1tZGMBhEoVCQl5cnhfxuEr5U2CO5ERs2bOD9998XJiWWL19OfX09hw8fpr6+/qrCDoVCrF+/nsHBQTZs2MBzzz2HxWLhxz/+McXFxcLr+/1+HA4HdrtdcE0++/vAwIDwaGtro7a2FqfTSTgcFiy4TCZDqVSSmppKVlYW2dnZZGdnk5mZKfxuMpmuyapf7Z/us5+Ly+XipZdewu12M3/+fMrLy4mNjf3Kry8xfnypsL1eLx988AHz5s0jIyNDCGnNmzePwsJCNm/ezMGDB1myZMmYPIlwOExdXR0pKSkUFBQwdepUTp48icvlGmXZIpEIJpOJjIwMwuHwmEcoFBrz9/DwMJcvX6a7u5uuri46Ozvp6emhp6eHixcvUl9fj9/vRy6Xo1Qq0Wg0WK1WcnNzycvLIycnR/g9MTFxzPv2eDw0NTXR1dVFOBymsrISv99PYmIifr+f1tZW3nrrLc6fP8/y5cv5yU9+QnZ29nXdGSRuPF8qbJfLxeuvv47NZuP5558XhB0Oh7l8+TIAR44cobm5mTlz5oy5PhAICP5vKBQiGAyOGRTKZDIUCsU1pX6Gw2GysrIIBAIEg0ECgYDw8Pv9+Hw+ent76ejo4Ny5c7S3t9PZ2UlzczP79u0jHA4TExNDbGwsqampFBUVUVRUxOTJk0lISKC7uxur1crf//3fA6DVavH7/fT29gKQlpbGL37xC1JTUzGbzSQlJQlukMTE84XCdrvd1NXVER8fzz//8z8TExMzyiLdfffd/Pu//ztNTU1UV1dzxx13jLrVy+VyysvLeeONN/j4449pbm7G6XRSVVVFb28vOp0OrVaLVqtFp9NhMBgwGo3CgPGLkMvlqNVq1Gr1554zefJkfD4fHo8Hj8eD2+3G4/HgdDq5ePEiJ0+e5OTJk1y6dIktW7ZQUVFBXFycYN2LioooKSkhLy+PtLS0UW6GQqEgJiYGjUYjWembENkXba7U3d3Nj3/8Y+bOncu3v/3tMRbV7Xbz3HPP8corr7Bw4UKef/55srOzhePhcJimpiaWL1+OVqvl8uXLaDQaDAaDYMVHIiNqtRqNRoNGoyEmJgaj0YjZbB7z0Ov16PV6DAYDBoMBvV5/zX5tKBTC4/EwNDSE0+lkYGAAh8NBV1cXp06dorW1la6uLoaGhoQU1pSUFIqLiykvLyc/P3+UWyZx8/G534zP5+P06dOcOHGCn/3sZ1cddMXFxVFUVITNZuP48eN88skno4Qtl8spLCwkPz+fY8eOsWbNGqZNm4ZcLsfr9eLxeBgeHmZ4eJihoSEGBwcZHBwUxHbmzBmCwaDgaoxYydjYWGJjY4mLi0Ov15OYmChERqxWK4mJiUIE5WoWVaFQCLOIycnJwvMej4eBgQH6+vro6emhq6uLhoYGWltbaW9v59ixY2zYsIG0tDSysrIoKiqitLSUgoIC9Hq9NDFzE/G5wh4YGGDPnj3k5+eP+vL/P5MnTyY7O5uamhq2b9/O4sWLsVqtwnG1Wi2I7IknnmDGjBkoFAoikQjBYBCfz4fP5xOEPuIyDA8P43K5hJ8ulwun0znqMTg4yKVLl/B6vYLfrtVqhRh4YmKiEBq0Wq3CVPhIfPz/C37kHyYlJYWSkhIOHTpEXV0dkUiEGTNmkJeXx6VLlzh16hQ1NTXs2bMHq9VKQUGB4Lbk5uYSHx8vWfMJZsynHwwG6evr48CBA7S0tJCWlkZLSwu5ubljfOyBgQHsdjsGg4GkpCQuX77Mzp07ueeee0aF/0pLS4UB1og7I5PJhEmarxr79fl8uN1uQegulwuHw0Fvb6/wsNvtDAwM0NHRQUtLC6FQCLlcjkajwWQyYbPZSEtLIy0tTYiBWywWLBYLWq1WeH/hcJidO3eyceNGHA4HSUlJrFixAoPBwIULF4S72fHjx6mpqeHjjz8mNTWV4uJiioqKmDJlCpMmTSIxMVES+QQw5hOPRCJ4PB7kcjmLFi1Co9HgcDiuGs/1+Xyo1WqWLVvGwoULkclkqNVqIUd5hJUrV+L1eq8aVrsWRnxws9l81eORSITBwUHsdjt9fX309vaOCgXa7XY6OjpoamrC7/cTFxeH2WwmOzub3Nxc0tPTBetuNpuFf4pIJCLcFUZmR8vLywmHw5w7d46mpiZqa2s5ceIEO3fuZNu2baSnpzNr1izKysqE105MTJTcFZH4wsHjjWL37t0MDg5yzz33EB8fP97NXZVAIIDD4aC7u3tUROTChQs4HA4cDgeAEE8vLCzE6/VSU1OD0+lkxYoV/NVf/RUWi+Wqrx8KhWhvb+fIkSPs27ePEydO0N3dTSQSITs7m7vvvps77riDzMxMUlJSpBnKcUYUYa9atYq2tjbefPNNSktLx7u5r0w4HGZoaIizZ8/S3t5OU1OTMCnjdDrx+/1otVrS09OZNm0aM2fOJCsrSwhJmkymq7oZgUCAc+fOcfDgQaqqqmhpaaG/vx+FQsH06dNZvnw5paWlJCUlkZiYKMW/xwFRhP3EE08Iwi4pKRnv5r4W4XCYrq4u2traOHbsGHV1dZw4cYL+/n4CgQBGo5GCggJmzZrFggULSE5ORq/Xo9PpUCqVYwakfr+f8+fP8/HHH7N582ZaW1sZGhrCZrOxZMkSVq1aRVZWFmazWRL4DUQUYf/lX/4lZ8+e5T//8z8pKCgY7+ZuOAMDA5w4cYLDhw9z4MABGhoacDgchMNhiouL+cY3vsHixYvJyspCp9Oh0WiuKnKfz0dzczMVFRVs3LiRnp4etFotK1eu5Fvf+haTJ09Gq9VKg80bgCjCDoVCRCIRYUX3rcxI8lNtbS2bNm1iy5Yt9PX1EQ6HKSoqYunSpSxbtowpU6YQGxuLQqG46oDR6/WyefNmXnvtNQ4fPkxsbCyPPPIIa9asYerUqahUKmmg+TUQRdgffPABdrudhx56aFSM+1ZmJCHL5/OxZ88eNm7cSGVlJZcvX0ahUFBUVMSyZct44IEHKCkpuaqbMZLQVVdXx5tvvsn27dsJhUKsWLGCZ555hrKyslveEEwUogh79erVnDp1ildffZWioqLxbk5UIpEIgUAAn8+H0+nkwIEDbNu2jZqaGnp7e4mLi6O4uJhVq1Zx//33k5KSMuY1AoEAXq+XCxcu8N5771FRUcHw8DBLly5lzZo1TJ8+XRL4NXJbR0VuNCNzAC6Xi76+Po4cOcLWrVs5fPgww8PDWK1WFi5cyCOPPMLs2bPH+NLBYBCn08nZs2fZuHEj27dvx+12s3jxYv7kT/4k6ozCeKL46U9/+tPxbuTcuXPEx8ezYMECTCbTeDc3YYzMpmq1WhISEsjJyWHevHksWLCAhIQEOjo6qK6uZteuXdTW1qLT6bBarajVamG5W2xsLBaLhZKSEmbPng18WvJi48aNdHd3k52dLeWlfAVEsdhdXV34/X5sNhsxMTHj3dxNRyAQoL+/n4sXL3L8+HG2bdtGfX09er2ekpISHn/8cebOnUtCQsIolyMQCNDb20tTUxPvvPMOBw4cIDU1lZUrV7Jy5UqSk5OlCMrnIIrF/uCDDzh06BB5eXm3ZandkWzClJQU8vLyKC8vF5LBjh8/TnV1NU1NTUQiEcxms5CzolAoMBgMZGRkUFxcTEZGBq2trezevZvGxkZUKhVJSUnExsZKPvj/QxRhP//889TU1HDfffdFTVTkehjJpbFYLBQUFFBYWMiUKVPQ6XScOHFCKLwTDAYxGo2CEVAqlSQkJDB16lSmTJmCRqPh0KFD1NbW0tHRgU6nw2w2o9FoJvgd3jyIIux3332Xnp4eVqxYgc1mG+/mbglkMhlGo5Hc3FxKS0vJzc0lHA7T0tLCgQMHOHfuHJFIBKPRKFhwlUpFeno6JSUlZGRk0N/fz/79+zl69Chutxuz2XzNC5ajFVGE3dnZSVJSEvfcc0/UV426HmJiYsjKyqK8vJycnBxcLhdHjhxh//792O12lEolJpNJsMhxcXFMnTqVoqIidDodbW1t7N+/n46ODvR6PWaz+bYcy3wWUYRts9koKysbVfdDYiyxsbFkZ2czc+ZMsrOz6ejoYO/evdTW1gqFhsxms1ByIiEhgWnTplFQUCBY77q6OiH3/GqLKW4XRBF2ZWUlx44dIycnR0rX/ArExsaSk5PD3LlzsVgsQmXX5uZmEhIShHWecrkchUJBeno606dPx2QyUV9fz8cff8zly5dJTU0lPj7+ttz4SRRhP/fcc+zcuZP77rtP8rG/IjKZDJ1OR1FREQsWLCASiVBdXc2HH36I1+vFZrMJCVMj55aUlFBWVkZnZydVVVXU1tYK5SS+aDV/NCKKsDdt2oTD4WDFihW3dVTkepDL5ZhMJubNm8fcuXM5efIkW7dupaamBrPZjNVqJSYmRrDeqamp3HnnnRgMBj766CO2bNkiLIW7nUpFiCLsU6dOYTAYuPfeez93WZfEFzMi2sceewyj0cjevXt5//33cTqdQvm2EZdDq9VSXFxMSUkJVVVVvPXWW8hkMoqKim6fmHdEJMLhsFhN3RacOXMmsmrVqojBYIjccccdkYqKiojX6x11TjAYjLS3t0cWL14cUSgUkYceeihy+vTpSCgUmqBei4coFvs3v/kNFRUV5OXlRXWuiJiYTCYWLVqExWKhtraWDz/8kMHBQfLz8zEYDMCnbozRaOSBBx4gHA5TUVHBrl27yMnJISUlJaojVKII++WXX6ahoWFMzRGJ60cmk6HRaJg6dSozZ86kp6eHLVu20NLSQnp6Ounp6cJ5I9tjZ2dns3v3brZs2UJcXByZmZlRu+GqNPN4CzMyRW+1Wpk+fToKhYLq6mo++eQTYmJiKCgoEFYtxcTEMGnSJKZNm8bRo0fZuXOn4J9PVOWA8UQUYXu9XnJycpgzZ85tmQQ13ozMTE6ZMoXk5ORRwi0tLRVmITUaDcnJyUybNk1Ioe3s7CQzMzPq7qSiCNtsNjN58mSp1O44IpfL0ev1QqH7zs5Otm/fTm9vL+Xl5cTFxQnF8ZOSkpgyZQp2u52amhra29tJSUkhNTU1aiImogj797//Pfv27aOwsFDKFRlnRup9T548mb6+PrZu3UpXVxdTp04dVeXWYrGQk5PD8PAwtbW1tLa2YrVaycjIiApxi5a2Wltby5IlSyQfWwRUKhUWi4X8/HycTicVFRV0d3czadIkYYpdJpORmJjIpEmTCAaDHDx4kJaWFjIyMqJC3KIIu6KiAofDwcMPPxx1vtzNikKhID4+npKSEoaHh9m0aRMdHR2kpaWNqj5lNpuZNGkSALW1tTQ1NZGTk3PLuyWiCLuvr4/U1FTmzp0rxFglxh+5XI7BYGDmzJl4vV4++ugjzpw5g81mw2KxCGmwBoOBzMxMIpEI+/bt4/jx4xQUFHxh+eibHVGEnZ6eTmlpKRaLRVqjJzIymYy4uDjmzJlDOBymqqqK5uZmUlJShDwT+FTc2dnZhEIhqqqqaGtro7S0dMw6zFsFUYS9fv16du3aRVFRkTR4nCBUKhV33HEHsbGxwprJkUjISOafXq8X9u3ZunUr7e3tzJo165ZcFS+KsF944QUOHTokDR4nGLlczrRp0zAajcJmVykpKaSnpws+90iqrNPp5P3336e/v59p06ah1WpvKXGL4heMbCt9K30w0YpMJuPJJ5/E5/Px/PPPC1scLliwQBB3YmIi//RP/8TAwAC///3vMRqN/M3f/A02m+2W+Q5Fsdgej4dJkyYJtzWJiUUmk1FaWoparWbHjh3C6qbPhvliYmJYuHAhx44d4w9/+IOwzvKWyS0RI4UwEAhE/H6/lLp6k+HxeCIvvvhiJCcnJ/LAAw9EWlpaRh0Ph8OR/v7+yP333x+Jj4+PvPLKK5H+/v4J6u21IYrFXrt2LevXr6e8vJyEhITxbk7iK6JUKsnNzSUSifDRRx/R3t7O7NmzhQH+SPLU7NmzqampobKykpycHLKysm761AhRHKbOzk7Onj2L1+sVozmJa8BsNvP000/z1FNPcejQIX72s5/R398vHJfJZGRlZfHLX/4Sg8HAv/3bv1FTU3PVzbZuJkQR9kgd6Mj4lwmUuEZkMhnJycmsXr2a5cuXU1lZyW9+8xt8Pp9wjkKhYObMmfzwhz/E6/Xy4osvcuTIkQns9Zcjiiui0+mYMWMGZWVlxMXFjXdzEtfISGZgWloaFy5cYMeOHcTFxY2qy61SqUhNTcXtdnPgwAEGBgbIy8u7aV1LUYQdDoeFDUxvtzIAtwoKhQKTyURqaipNTU3s3buX7OxscnJyBHHHxsaSkZHBhQsX2L9/P0qlkqlTp17zXvZiINrM4969eykrK5PWPN7EqFQq4uPjSUxMZO/evdTX1zNr1izi4+OF+LXRaCQpKYmWlhaOHDlCUlIS+fn5N11RHlF87IaGBvbt28fg4KAYzUl8DfR6PQsWLOB73/sera2t/Nd//Rd2u13Yq14mk1FeXs7q1atRKBT87ne/o6GhYYJ7PRZRhG00GklISLjpQ0QSn2IwGPjmN7/JypUr2bBhAxUVFbhcLuG4Wq1m/vz5PProo3R1dfHqq6/S2dk5gT0eiyiuiN/vJycnh/Lycql23y3AZ1fA79mzh9raWqZNm4bNZhOyM+Pi4rBYLHR3d/PJJ5+g1+spLS29abI3RRH2SL6vtL3yrcNITZKkpCQ2bdpEZ2cn5eXlo/ztkXrcBw8e5NChQ8yaNeuqu6JNBKII+9e//jUVFRVMnz49Kpf6RytyuZyCggK6urrYvHkz8fHx5OfnC/kiI6WMdTodO3bs4OLFi9x33303xc4KovjYZ86c4dixYwwPD4vRnMQNRCaTsXbtWgoLC1m/fj2HDx8eNXmj1Wq58847uf/++9m3bx8bNmwQBpoTiSjCVqlUqNXqWyblUWI0FouFH/3oRygUCtatW8fx48dHzSJnZGTw3e9+F4vFwq9+9Ss6OzsnfJZZFFckMTGROXPmCNU+JW49srOz6evrY/v27cTFxVFUVDTKJdHr9dhsNt5++20GBgZYsmTJhMa2RRF2bGwsSUlJo0rdStxayGQypk6dytGjR6muriYtLY3CwsJRU+5ms5menh7ef/995s+fj81mm7DvWxTf4LnnnuOZZ57h7NmzYjQnMU5YLBaeffZZTCYT7733Ho2NjcIxmUyGxWLh+9//PgaDgZ///OcMDQ1NWF9FEfaVK1fo6uoaNeiQuPWQy+XMnTuXJUuWcPr0aT788MNRKa4qlYrc3Fx+8IMfcODAAbZs2TJh4hZt8KjRaKTBYxSg0+lYtWoVxcXF7Nixg6qqqlHHY2Njefzxx5k1axbr1q2jq6trQqIkovjYycnJzJs3j6lTp972+w9GAwaDAYVCweHDh+nt7WXGjBlCcttIHZOkpCT+8Ic/YDAYmDJliujpyqKYUK1Wi9FolCx2lKBWq5k3bx7z58+ntbWVnTt3jrLKcrmcu+++m/nz57Nx40ba29sJBAKi9lEUpb377rv893//N1euXBGjOQkRsFqtLF26FKvVyqZNmzh37tyo43FxcXzve9/D6XSyadMment7Re2fqDOPn80Qk7i1kclkFBcXs2zZMmGbkFAoNOqcWbNmcd9997F7926am5tFDR6IIuzk5GQyMjIk/zrKMJlM3HPPPRQUFPDBBx9w/vz5UcdVKhWrV68mEomwbds2UVNbRVvzWFZWRl5enjTzGGUYDAbUajWVlZXI5XLmzJkzaixltVrp6Ohg3759ZGRkMHnyZFFSW0Wx2BkZGeTm5kqijkJiYmIoKSlh+vTpvPvuu1y8eHHUcblczsqVK1GpVFRWVo45Pl6IIuyf/OQnfPvb36a9vV2M5iREJj09nSeffBK3280bb7wxJm5dUlLCzJkzqauro6amRpQIiSjC9ng8uFyuMYMLiehArVaTn5/PggULePPNN+nu7h6V3adQKHjwwQfRarXs2rVLlNQK0QLLMpnsliwgLvHVsNlsrFmzBrfbzYsvvjimUtTcuXMpLy/nwIED7Nq1a9zTWkUR9r/+67/yzjvvMHnyZDGak5gAlEolGRkZLFmyhNdee41Lly6Nckk0Gg2LFi0iPj6e6upqTp8+Pa79EUXYg4OD2O120WefJMTFbDazevVqhoaGeOmll0atmJLJZMydO1fYGbi6unpc+yKKsF999VV+/vOf09XVJUZzEhOEWq2mqKiIu+66i7fffptz586NMmaJiYnMmzcPlUpFdXU1ly9fHre+SGmrEjcMmUyGwWDgO9/5Dv39/bz22mujiiQpFArmzp1LWVkZzc3N1NbWjltfRBF2SkoKWVlZ0szjbYBarWbBggVMmTKFLVu20NHRMWogmZGRwbx58/B4PGzdunXcFniLMvNotVqZOXMmubm5N8XSfInxY6TYzvDwMDt27MBisVBUVCSkrSqVSmQyGceOHePMmTNMnz6d9PT0G94PUSy20+nE4XDc9MXCJW4MCoWCRx99lJSUFDZv3kxnZ+eoCElubi7z58/HbrezdevWcVmIIIqwN2zYwCuvvCJ66qLExCCTycjOzmbp0qVcuHCB2tpanE6ncNxkMlFeXk5iYiLV1dXjkhwlirB7e3vp7OyUBo+3GU888QQmk4mNGzfS0dEx6lhubi533XUXnZ2d4xL6E0XYWVlZ5OfnS7sZ3GZMnz6dGTNmcOLECVpbW/F4PMIxm83GvffeSyQSYePGjTd8fyJRhL169WrWrl0r7cp7m6FQKHjssceEzL7PuhxqtZrc3FwKCwtpaGjgxIkTN7RtUYQdDAalWcfblHvvvZesrCxqa2tpbW0dlQiXkpLCsmXLcLlcVFRU3NB2RRH2L3/5S5599lmpYM5tiMlkYtmyZTidTurq6hgYGBh1bM6cORiNRrZs2XJDx2BSdp/EuLN06VIyMzPZu3fvGJcjISGBu+66i46ODg4dOnTDQn+ilV/Q6/VS3b7blLy8PKZNm8bZs2c5evToKHckISGBZcuW4fV62bhx4w3L2RdF2C+88AIbN24kLy9PjOYkbjLkcjmLFi0iKSmJw4cPj1pJFRsbS3FxMRkZGWzevBmfz3dDcrVF2TCksrKSw4cPEwgEvtQd0Wq1fPe73yUrK0tyXaKIWbNmkZeXx9GjR2lsbBSMnEwmw2Qy8Y1vfIPXXnuN/fv3M3/+/K+9H6howq6srESj0XxuhyORCKFQiJiYGB566CEyMzMlYUcRCQkJ3HHHHTQ0NFBXV8fSpUsxGAzAp1vwPfjgg6xbt47NmzczZ86cW0PYTqcTjUbDP/zDPzBp0qSrnjM0NMTOnTvZsGEDfr9fjG5JiIhCoeDOO+9k+/btHD16lLa2NmbNmgV8urqmsLCQnJwcPv74YzweD3q9/msZNlGEXVhYKGyMmZ2dfdVz+vv7OX36tJQoFcXk5+dTUlLCli1bqK2tZebMmUK0TK/XM3/+fH73u9/R1taGyWT6Wpmgogwev/0Ukj0AAAkySURBVPnNb/L973+fpKQkMZqTuEkxGo1Mnz4djUZDfX39qFqOGo2G+++/n1AoRHV1NW63+2u1JYqwT506RVNT09furMStT2lpKQUFBZw8eZIjR47Q09NDW1sbbW1t6HQ69Ho91dXVX7vOoyiuyNtvv82JEycoKSkhNjaW/v5+fD4fGo0Gk8mEUqnkwoULwn9wIBDA6/XS09NDKBRCoVBgs9kIhUIMDAwI15rNZpRKpbBLlUwmIz09nWAwSG9vL8FgEJVKRWJiIpFIhP7+fvx+PzExMSQmJhIMBunp6QE+9QEzMjIYGhoScsfj4uKIj4/H5/PR19dHJBJBo9FgtVrx+XzCmj21Wk1KSgpDQ0MMDg4SDAbRarWYzWb8fr+QrjtyntvtFp6LiYkhKSkJl8vF4OAgoVAIrVaLyWQiEAgI5ymVSrKysnA4HPT39xMOh4mLiyMxMXHMtWazmUAgIPRPpVKRmZnJwMAADodDOC8+Ph63201/fz+RSITY2FgSExPx+Xyj+pyWlsbAwABOp5NQKIROp8NsNuN2u7Hb7cL7sNlsDA8PC99jbGwsVquVwcFB3G43MpkMo9FISUkJ9fX1rF+/nqysLOE78Pv9yGQympqaaG9vJykp6brdEVGE7fP5GBgYIBAIcPbsWd59910uXbpESkoKK1euRK/X8z//8z80NDQQiURwuVx0dXXxwgsv4HK50Ov1/MVf/AXDw8N8+OGHdHZ2kpqayuOPP47RaOTXv/41fr8flUrFT3/6UwYGBli/fj0DAwNYLBZWr16N1+vlww8/pLu7m0mTJvH0009jt9t5+eWXhbV6v/jFL6ivr2fr1q04HA7y8/NZtWoV586d47333sPn85Gens6zzz7L+fPn+e1vfwtAamoqf/d3f0ddXR07duzA4XBQWFjIY489RkdHB+vXrwc+XUn0j//4jzQ3N/Pmm28SCoXIzs7mT//0T6mrq6OqqorBwUGKiop4+OGH6e7u5tVXXxUE8cILL3Do0CEqKirwer3k5+fzrW99i4aGBiorK3G5XBQVFfHoo48K7crlchITE/nVr37FgQMH+Oijj3C5XBQWFvLEE0/Q2NjI1q1b8fv95Ofns3r1ak6ePMmbb76JTCYjNTWVH/3oR+zbt4/du3czNDREWVkZjzzyCC0tLbz33nvApxmcf/3Xf019fT1//OMfgU996meffZa9e/dy8OBBwuGwsImtTCZj+/btpKSkCLs2X7lyBY1Gw5UrV9i2bRsFBQXXnTgnirAzMzNxOBzExsYyMDDA2bNnOXPmDF6vF6fTiVwu58KFCwCUlZWh1+vxeDycPHmSwcFBTCYTLpeLoaEh2tvbOXv2rHCtWq2mtbUVn8+HWq3G5/MxNDTE6dOn6e3tFSypx+Ohvb2d8+fPI5PJ8Hg8DA4OcuLECWQyGWazmWAwiN1u59SpU/T19RETEyNYtNbWVrxer3A3GbkWPq105ff76evrE64deQ8Oh0M4b2hoiEAgwMDAAK2trcJA2efzceXKFU6ePEl/fz8GgwG32z3q2pG7jt1up62tDbfbjUajGXXt4ODgmHblcjnJycmEw2H6+vpoa2vD6XQK54085/V60Wg0eL1e+vv7hc/F5/MRCoXo7e3l5MmTOBwOEhIS8Hq99PX1Cf2LRCIEAgHsdrvwnEajIRAI0N3dTUNDg7BfzeTJk7HZbHg8HmbPns3ixYtJTk6mp6eHt956i7q6OuHuer3IIiLsNDlSUyQ+Pp5wOMzQ0BDBYBClUolOp0Mul+NwOAiHw8jlcsxmMwADAwPCcyaTiXA4jMvlGnWtQqEQbofw6c5WwWBQuG0qFAoMBoNwJxhxTwwGA6FQCIfDAXw6O2axWIRybOFwGLVajV6vJxAICCtAVCoVRqORYDAoXKtUKjGbzXi9XoaHhwmHw2g0GnQ6HcFgUFiprVQqBddm5LmR1/N6vbjd7s+9Vi6XY7VacblcuFwuIpEIarUag8HwpdcqFAosFgsul2vUeXq9Hp/PN+b1/H6/8H6VSiUJCQkMDw8L18bExKDVavH7/cLmSSPb4Y0YHPjUjTGZTIJ753a70Wq1eDwe3nnnHd555x2GhoaQyWRYrVY6OzuFPdyfe+45lixZgl6vvy7NiSJsCYn/j8/n48KFCxw5coTz58/j8/mEscDs2bPJzMxEpVJd9+tLwpaYcEYy+j6bAToSDLhepN2OJCYUv99PR0cHx48fHxXiGx4e/lqTdaIMHiUkPovdbmf37t3s2rULpVJJdnY2g4ODnDp1CrPZTEZGBhcuXGDt2rXk5uZeVxuSsCVEpaGhgZdffpmLFy/yzDPPMH/+fFQqFeFwGK/XS3NzMz/84Q9xu9382Z/92XW3I7kiEqLR2NjIf/zHf3D06FGWL1/OkiVLSEpKwmw2k5CQQGpqKnfffTdr1qwB+FquiCRsCVHweDx88MEHVFVVkZ+fz4MPPojRaBxznlar5cknnyQ3NxelUnndiw4kYUuIQnNzM5988gk+n4+CggLS0tI+91ybzcZTTz2FXq+/7jWQko8tIQr19fVcvHgRm832pVviyWQyFi1ahF6vv+5tyiWLLTHuhMNhjh8/jt1ux2azfaG1HiE5ORmdTnfdsWxJ2BLjTigU4tKlSwwPD6PVakXZ71MStoQoRCKRcd8p7LNIwpYYd5RKJXq9HpVKhdfrFaXqriRsiXFHJpORlpaGXq+nr69PlDrpkrAlRGH+/PlkZmbS29vL+fPnv3Tyxefz4Xa7r7sylCRsCVGYOXMmpaWlOJ1ODh8+TEdHx+f63KFQiMbGRnbs2CEsTrhWJGFLiEJiYiJr1qxh9uzZVFZWsm7dOtxu9xhxRyIRWlpa+O1vf8vkyZNJSEi4rvakfGwJ0RixxM8//zy7du1i6tSpPP3009x9991otVq6urrYv38//f39fOc73yEjI+MLJ3K+CEnYEqISCATo6uqiqqqKqqoqrly5IqzqLysr46677mLGjBmYzeavVZ1XEraE6IRCIdxuN4ODg/h8PmFd60i56bi4uK9dt1EStkRUIg0eJaISSdgSUYkkbImoRBK2RFQiCVsiKpGELRGVSMKWiEokYUtEJZKwJaISSdgSUYkkbImoRBK2RFQiCVsiKpGELRGV/C/K3wL+0BMg2wAAAABJRU5ErkJggg==)
physics-General
physics-
A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg.
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ePH8dms6FSqQgODsZgMKDRaIiIiCA0NJTc3FxiYmIwmUyj8k1VqVSEhYUxc+ZM3n77bXbu3Mk111wzKl/LhebxeOjr6+P9998nOTmZO+64A5PJFOhmDbtBd/MURaG9vZ1nnnmGkpIS2tvb/T/T6/V8+9vf5sYbb6S+vp633nqLXbt2kZaWxq233sry5ctxu938/ve/5/LLL+f3v/899fX1o7p7NHPmTPr6+vjzn/9MT09PoJszIvX397Nz505kWWblypUEBwePyXG5QYeppaWFP/7xj7hcLtRq9Te6ciqVisTERDIyMtBoNERHR7N48WIyMjLIyMjgjjvu4P777wfgxRdf5Nlnnx3VC5RkZWWRnp5OUVHRqP9iuBBsNhsVFRWUlZWxbNkywsLCxkwp/OsGHCZFUbDb7ezfv5/jx4+zaNGi03ZpJElCp9NhNBrRaDRoNBoMBgMGgwG9Xk9kZCSLFy8mKyuL9vZ2tm7dyoEDB4b1RV1M8fHx5ObmYrfbOXDgAE6nM9BNGhG8Xi8Oh4PKykp27tzJtddeS0hICCqVCrfbTX9/P83NzVRVVY2ZL6BBhamxsZH9+/ezYsUKIiIihlxACAoK8q9D19XVRXV19ZAeZySIjIwkJycHjUZDaWkpHR0dgW5SwHm9XpxOJyUlJWzdutU//66lpYUTJ05QU1NDVVUVL730Etu2bRszM0gGVIDwFR3Wr19PTEwMs2bN4vjx40N+UofD4f9G0mq1BAcHD/mxAk2SJJKTkzGbzRQWFnL48GFiYmIC3ayA8o0lPfTQQzQ0NAB8oxejKApTp07liSeeGDMDtwMKU09PD9u3b6e9vZ0bbrgBo9E45DfA4/FQW1vLoUOHUKvVZGZmMnv27CE91kgRFxdHfn4+n376KeXl5SxcuHDMfECGwuv1Ul1dzdy5c8+6a8j06dPJyMgYM8WIc4bJ5XJRX1/Pxo0b+clPfkJCQsKA1z5QFAWPx4PD4aC7uxu3201XVxcbNmzA6/VyySWX8Nhjj5GUlHTeLySQzGYz3/3udyksLGT//v04nU50Ot2YPdE+F71ez/XXX8911113xkmskiQRFBREUFDQRW7dhXPOMHV3d/Ovf/2L3NxcoqOj0el0Aw6Tx+OhubmZrVu3EhISwuHDhykqKsJsNvPII49wzTXXEBsbO6oHb+GLc8ArrriC6OhoKioqOHny5Bkneo4HOp1uQONtY+3L5oxhUhQFr9fL7t27OXr0KA8++CAGg2FQb4AsywQHB2OxWNDr9ezYsYPq6mruvPNOli5dSkxMDBqNZtS/qbIso9VqycjIYM+ePbzzzjvcdtttY/YKXI/Hg91up6enB5vNRk1NDQ0NDbS1tdHW1kZnZyc2mw273Y7X60WSJGRZ9s98CQ4OJi4ujqSkJBITEwkLC8NkMmE2m0f1keqMYfJ4PDQ0NPDyyy8zY8YMSkpK/B96h8NBeXk5drudxsZGPvjgA6KiokhLSzvlAyTLMiaTiXnz5hEUFERFRQXPP/8877//PvPnz8dqtaJWq0d9mOCLb9np06eza9cu3nnnHf+55Wjndrv93fSOjg66urpoa2ujqqqK8vJyqqqqsNlsuN1uXC4XNpuN3t5evF6vf11BSZJQFMU/m1ylUvmDpdVqiY6OZuLEicyYMYP09HQiIyMJDw8nKCgIo9F4xhnoI80Zw+RyuaioqODo0aNs2bLllBfjW3nG4/FQWFjI9ddfz7e+9S1eeOGF036AVCoVUVFRrFq1irKyMrZu3crPf/5zEhISSE9PP+UCstHKtzaE1Wrl0KFDtLS0EBISMioLEb5zXY/Hw8mTJ9m1axc7duygvLycEydO+Pf21el0JCUlkZGRQUJCArIs88477+B2u4mKijrr4/f09NDe3k5ISAhNTU0UFxezbt06LBYL6enpTJkyhblz5zJ//nzCw8PRaDTIsowsyyM2WGcMk0ajISUlhTvuuOOUKUPwxfSQgwcP8umnnxIdHc0NN9zAhAkTMJvNZ3wiX5fvkUceoampidLSUp5++ml++ctfMmHChBH7Bg2UJEnMmDGDtLQ0tm3bRm1tLampqaMuTG63m+7ubo4cOcJbb73Fu+++S0tLCyaTidDQUNLS0rjhhhuYPn06WVlZhIaGotFo8Hq9nDhxgvfee4/ExERWr1591ufYuXMnW7du5cYbb2TVqlX+S1k+/vhjjh8/znvvvceGDRvQ6/Xk5uaydOlSZs+eTXx8/Ig94p8xTLIsk5SUxB133PGNgkNvby8bNmzg4MGDTJw4kR/84AcYDIZzHmHUajVTp05lxYoV1NTUsGXLFjIyMrj77rvP+k02WoSGhpKdnc27777L7t27mTZtGpGRkYFu1jl5vV5cLhfHjx9n9+7d7Nmzh3379tHT00NwcDBXXnklc+bMISsri9jYWH/3S6fT+Zc5c7lcdHR0+M8fQ0JCzvh8LpfLf9WAwWAgOjqamJgYUlNTWbZsGSdOnKC8vJzS0lIOHjxIaWkpJSUlJCQkcMUVV7BkyRJSUlL8XcCR4qxh0mq1p63K+KYL+S6niIiIOOXnvuKFx+PB7Xb7p4tIkoTJZOKqq66iurqaNWvW8Ne//pXY2FhuvvnmUd/dU6lU5OTkoNVq2bx5MzfddNOID1NfX59//tyzzz5LcXExXV1dhISEcM011/Cd73yHqVOnYrFYLmjV1fdZCwkJITExkblz59Lb28uJEycoKirirbfeYs+ePVRXV/P+++9z9913U1BQQHBwMDqdbkT0AIZ9dSJFUXA6nTQ0NOBwOKitraW/vx9FUfxduZiYGB544AH2799PUVERzz33HKGhoSxcuHDUL66RlJREbm4uO3bsoKysjMmTJ4+IP/TpeL1e9u/fzyuvvMKbb76JwWBg2rRpLF26lKuvvtpfIApEAUClUmE2m0lPT2fSpElce+21lJWV8cYbb7Bz504eeOABFi5cyD333EN+fv6IqAIOKUxqtZqIiAiSk5OJjY313+50OikqKqK8vJyWlhYmTZqERqPhtddeY9GiRcyePRuz2ewvSDz66KM8/fTT9Pb28tprr1FZWUlycjJer3fUhioiIoJbbrmFXbt28dFHH3HVVVeh1+sD3axTeDweOjo6WLt2Lf/85z9pbW1lwYIFLF++nJkzZxIbG4vJZAr4SrWSJKFWq1Gr1Wg0GmbMmEFycjI33ngjO3bsYMOGDfz85z8nPz+flStXkpKSEtDrpIb0bmk0GhYuXOjv0nxVRkYGsbGx5Ofn+0ujBoMBk8l0yodKr9ezaNEisrKysNls/vu1t7eP2iABmEwmZs2aRUREBPv27ePYsWOkp6ePqAKLoigUFRXx17/+FY1Gw2233cbKlSuJiorCYDAEunmn5Runio2NxWq1kpWVxSWXXMKaNWvYtGkTJSUl3H///eTl5RERERGQIZchH5kiIyO/cT7w1X7vuciyjMFgIDEx8ZTbvV7vqBlXOB1ZlgkJCSE5OZnKykq2bNky4hapVKlUZGVlsXTpUr71rW8xb968UXWFsFqtJiQkhKVLl5KWlsbrr7/OmjVreOSRR/jOd77D6tWriYuLu+gTAkZmZ36UCwoKYv78+Xi9XgoLC0fclp2SJGG1Wnn00UeZO3fuqJ3OJUkSKSkpPPjgg6xfv57U1FTeeustbrvtNvbs2UNnZ+dFbY9YHvkC0Gq1XH755bz++uscOXKEkydP+k/mRwq1Wk1oaOiwPqZv2lB7ezs7d+484/08Hg9Hjx4dluuYdDodGo2GOXPm8Otf/5p169axdetWfvjDH3LvvfeybNkyIiMjL0oRaOT8dccQtVrtH9Tcs2cPZWVlWCyWERWm4eZbqTUmJoaKigreeOONM95XURRcLhdms3lYijO+86lZs2aRmJhIZmYmTz75JH/4wx9QFIWbbrrpohRUxu5fN4B8VaiCggI+/PBDXnrpJaZMmTIiyrcXiiRJGI1G8vLymDBhwoDubzabmTZt2rCdT0qSREREBDfffDMRERH85je/4YknnsDhcHDTTTdd8Is2RZguoNmzZ5OSksL27dtpbGwkNjZ21BZWzsW3kdkDDzxwznUwfO+BLMvodLphLc6oVCoMBgMFBQVIksSzzz7L888/j9frZcWKFRd0po0I0wUUGxvLvHnzKC4upqioiEsuuWRUVc0GQ5Ik/1qCgSbLMhaLhYKCAkwmE6tXr2bt2rWEh4fzne98h6CgoAtSXRXVvAsoOjqaBQsWoNPpOHDgwEWvLo13wcHBzJkzh6effhq1Ws2///u/s3nzZux2+wV5PhGmC0iSJJKSkggJCeHTTz+lqKgo0E0ad3Q6HfPnz+fBBx9Ep9Px+OOPU1JSQm9v77A/lwjTBRYbG0teXp7/spOxskbcaKFSqTCZTFx99dXcfffd2Gw2fvOb31BRUeGfoTNcRJguMJPJxMqVK1GpVOzduxen0ykCFQBWq5WbbrqJ6667jgMHDvDiiy/S3t4+rIESYbrADAYDixcvJjExkYqKCo4dOzZmFl0cbcLDw3nwwQeZPHky27dv59VXXz3rUmSDJcJ0gfnKv7m5uXR2dvLyyy9fsBNg4ew0Gg0JCQn87Gc/w2q1snbtWg4cODBs508iTBdJbm4uQUFB/O///i8dHR0jaq7eeOEbTM/NzWXlypXYbDaee+452trahuXvIcJ0keTm5jJjxgza29s5evSoCFOA+K72XrhwIUuWLGHnzp3s2LFjWM5jRZgukpiYGKZNm4bL5WLXrl3fWKRGuLhiY2O599570ev1bNy4kaNHj573Y4owXSS+8yaj0ciHH35IY2NjoJs0run1eiZPnsz999/P559/zj//+c/zvlRGhOkiSk5OJicnh5KSEoqKikSJPIB8E3NvuOEGEhMTWbduHSdOnBjw0t+nI8J0EVmtVr7//e9jMBj4+OOPR9xFg+ONSqUiNjaWnJwcenp6WLt2LV1dXUN+PBGmi0iv13PJJZcQHR1NUVERRUVFwz4KLwyc7xqsBQsWEBERwaZNm6itrR3yOKAI00WkUqkICQkhMzOTzs5O3nvvPTGAOwJkZGRQUFBARUUFO3fuHPK4kwjTRabRaLj00kuRJIldu3bR29srunoBFhISwvXXX49Go+G9996jubl5SI8jwnSRaTQarrzySuLj46mtraWxsfG8TnqF86dSqUhISGD+/PnU1NRQVlY2pMcRYbrIZFkmPj6eBQsW0N3dzdtvv013d3egmzWu+Sp73/72t3G5XOzcuXNIxSERpgCQZZklS5ag1+t56aWXqKurC3STxj2DwUBeXh4Gg4FDhw7R2to66KELEaYAycjI4Nprr6W1tZW9e/eKMacA02q1TJkyhaioKJqbmzl48OA517L4OhGmAAkNDWXRokVotVq2bdvG8ePHA92kcU2WZYKCgpg5cyZOp5ODBw8OutIqwhQger2erKws4uLiKCsrY+/evYFu0rgnSRLz5s1Do9FQVFQ06MKQCFMAhYeHc9lll9HS0sKOHTtEiXwEyMzMxGq18tlnn4kwjSZBQUHcddddhIeHc+DAAWw2m5gREWAWi4WsrCxaWlqoqakZ1HmTCFMAaTQaJk+ezKxZs2hoaOCdd97B4XAEulnjmtFoZMKECbjdbo4cOTKoy9pFmALIt3Dj3Llz6e/v59lnnxVr6wWYTqcjNjYWlUpFdXW1CNNoM3fuXKZPn05VVRU1NTXi3CmAfPtrRUREcPToUfr6+gb+uxewXcIApaamMmvWLPr6+tizZ895XQYgnD+z2YzVaqWurk6EabSxWCzMnz8frVbLhx9+SG1tbaCbNOZ4PB6cTicOh8P/r6+vD5fL9Y0Bc4PBQEhICL29vf4tYgdCLNw/QqSlpZGTk0NhYSG7d+8mKysr0E0aU7q6uqiurj4lHCqVivDwcCZMmIDRaPTfrlar0el0eL3eQVXzRJhGiPDwcH76059y++23s2nTJm655RZMJtNF2fHuQlAUBY/HQ3d3Nw6HA51OR3BwcMB2AVLD70QAABHQSURBVNHpdLS2tvLCCy9QX19Pf3+/f6Wi6667juXLl5OQkIAsy6hUKjQaDR6PZ1BjTSJMI0RQUBC5ubmkp6dTVVXF1q1bufrqq9HpdIFu2qApikJ/fz9FRUX84x//oKWlhaioKG655RZSU1MDsoeu1+tl6tSpXHXVVfzpT3/i2LFjOBwOJEni+PHjlJaWct9995Geno6iKOj1eiRJGtS4nwjTCCFJEjqdjpkzZ1JaWsratWspKCgYtWGqr6/ngQceoLy83H+UqqysZPny5VgsloC1zWq1snTpUt59911KSkpwu900NTWxfv16CgsLeeCBB5g3bx6RkZFYrdZBPbYI0wiiVqtZvnw5u3btoqqqisbGRkJCQi7IxlwXksfjobGxkY6ODjwej/8Ef8eOHRQWFgb89fT399PX13fKRFaXy0VNTQ3/+Z//yebNmzEYDDQ2Nooj02glSRKZmZnMmTOHv/zlL2zatImoqCgiIyMD3bRBkWUZq9WKxWKhtbXVX16OiYlh0aJFmM3mgLXN4/FQV1fH7t27aWho8N+u1WqJjIxk0aJF5Ofns3XrVoBBBV+EaQSRJAmDwcC1117Lm2++ydq1a7nqqqtGXZh8S2jdfvvt/OlPf8Jut+NyuVi+fDkPPvjgGbtPiqKgKAput/uM13fJsuz/J0nSgPcI9ng89PX10dDQwFNPPXXK4xkMBqKionjwwQe5/vrr6e7uZsuWLahUqkEVTESYRqC0tDSWL1/Oyy+/zPbt28nKyhp1G0sbjUa+//3vk5uby8GDBwkNDWXx4sWEh4efsULp8Xjo6enh2LFj2O32bwTKt0N7cHAw4eHhmM3mAVc7bTYbu3bt4sknn6S0tBSHw4Esy5jNZpYuXcrq1avJzMxEo9HQ3d2N0+lEluVBFUtEmEagkJAQrrjiCl5//XU2b97M5ZdfTlpaWqCbNSi+b/ycnByys7P9/z9bt0mWZbRaLVqtlj//+c8UFhYiSRITJkzwFwWOHj1KWVkZKpWK5cuXk5eXR0RExDm/bBRFwWAwcOedd/o3nJMkidDQUGbNmkVsbCx6vR744vypt7cXjUbjv20gRJhGIL1ez9SpU0lNTaW6uppPPvlk1IUJ/q/bajAYBnx/o9HIxIkTWbhwIX/729/weDzcfvvtXH/99QQFBdHe3s66det4+eWX2bdvH3fffTff/e53iYqKOmugTCYT+fn55OXlnfJ8KpXK32X0sdlstLe3Ex8fj8lkGvDrHZ0jguOAxWLh8ssvp7Ozky1btoybya+SJKHX6wkLC8NqtaLT6bBarcTHxxMaGsrEiRO54447uO6662hsbGTNmjVs27btnGto+M5/dDqd/59Wq0WlUn0jhD09PTQ1NTFhwoRBDU2IMI1Qvi5JXFwcJSUlNDc3D3qBj9FMkqQzng9ZLBby8/PRaDS0t7ezffv2YfuycblctLa2YrfbmThxogjTWKBWq4mJieGyyy6jp6eHZ555Rqyv9yXflB/fDIX+/v5hC5PD4aCmpgaASZMmiTCNFbIsM3/+fCwWCy+88IK41ulLTqeT48eP4/F40Ov1pKamDlu1s7e3l4qKCvR6PWlpaSJMY8mcOXO48cYb6enpobi4eNwv9K8oCnV1dXz00Ue43W5mzJjBtddeO2wTghsbGzly5AgZGRkEBwcPatBWhGmEs1gsLF68GLPZzAcffEBlZWWgm3TR+AZwOzo6qK2tpaqqik2bNvGHP/yBkydPcvvtt/PYY48xadKkYTsy7dmzB5vNxqxZs1CrB1fsFqXxEU6lUpGens7NN9/Mtm3bKCkpYerUqaNuEHeovF4vmzdvprOzk0OHDrF//34mTpzIz372M2bOnEloaOiwTAb2TcbdvXs3ANOmTRv07HZxZBoFIiIieOqppwgNDWXTpk3jZjkw32ZkBQUFLFu2jKlTp9Ld3U1dXZ1/rYbhmlXv8Xhobm6mqqoKs9nM1KlTRZjGIlmW/Ze2l5SUsH79eux2e6CbdVFIkkRkZCQpKSncfvvt5OTk0NLSwu9+9ztaWloGtXrQ2fT391NcXEx3dzcJCQmkpaUNupsnwjQK+Ebqr7zySiIjI3n11VfH1aIrKpUKg8FAXFwcq1atIj4+nv379/PUU09RX18/LBVOh8PBxx9/jNvtJjc3F6PROOiihgjTKHLppZdSUFBAaWkpFRUV43IQd/78+axatQqtVssbb7zB+vXrsdls5xUor9dLb28vmzdvxmg0kp+fP6RzUhGmUUSr1XL11VdjsVh47bXXqK+vD3STLjqdTsfixYu5/fbbURSFV199lc2bN5/Xljz9/f0cPHiQiooKZsyYQWJi4pAeR4RpFPHNoL7rrrvYuXMn+/btG5P7OimKQl9fn/9SiK+uXSfLMhEREXzve98jIyODtrY2nn32WQoLC+np6RnSEaqlpYXXXnsNo9HIFVdcQWho6JDaLcI0yoSGhvLtb38bSZJ45ZVXaGhoGDOzInzjSjabjZaWFv8Mh7a2Nrq6uujv78fr9aLX65k8eTJPPPEEkZGR1NTU8PTTT1NaWkpPTw8ej2fA74nX62Xfvn2UlZWRm5vLrFmzCAoKGlL7VY8//vjjQ/rNC6Sjo4NNmzbhcDi4+uqriY+PD3STRhRZllGr1RQWFlJcXIxarSYvLy/g6yoMB6/XS3t7O3v37qW8vJzk5GQyMzORZRm73Y4sy4SGhqJSqVCpVMTHxxMREYHJZMJisdDQ0IDH4yEiIsK/utC5ns9ut/PCCy9QWlrKj3/8Y6ZPnz7kcrsYtB2FTCYTDz30EKtWreKf//wnN910EwkJCYO6kG0kkmWZ8PBw8vPzycnJ8a9Z99XLJ3zlakmS/OeQixYtAr6YHKzVajEajQMqIDidTg4dOsTBgwfJzs7m8ssvH/C1V6dt/5B/UwgYjUbD7Nmz+e53v0t3dzdPPvkkLS0tgW7WeZMkCbVajdlsJjw8nOjoaKKjo4mMjMRisaDX608pV8uyTHBwsP9+ERERBAcHo1arzxkm3zSlP/7xj3i9XlatWoXFYhn02NJXiTCNQr4L6JYuXcrs2bN54403ePfddwe1yPx453A42LZtGx988AF5eXnk5OSc9xQtEaZRLDk5mZUrV2I2m3nllVfYtWtXoJs0KiiKQnl5OWvXrvVfMzYcC2OKMI1iOp2OnJwcHnnkEVpbW3nllVeor68fV4O5g6UoCi0tLfz973+nurqaG264gezs7PPq3vmIMI1ywcHBrFq1itzcXPbs2cNzzz1HV1fXuJkMOxher5e+vj42bdrEO++8Q0JCAnfeeeeQx5W+ToRplFOpVAQFBfH973+fCRMm8NJLL/H222/T29sb6KaNOE6nk5KSEp555hl0Oh3/9m//RlhY2LBtJCDCNAZIkkR2djaPPvooMTEx/Nd//RdbtmwZ1rURRjuXy0VdXR1PPvkkfX19LF++nEsvvXRYt7gRYRojTCYTs2bN4mc/+xlOp5Nf//rXfPzxxzidznEdKN+siqqqKp5++mk+/fRTlixZwq233kpISMiw7n8lwjSGhIWFsWzZMlasWEFDQwOPP/44x48fx+VyjctA+YLU1NTEb3/7WzZu3Mi0adN4+OGHL8jMGhGmMcZgMLB69WpuvfVWjh07xi233ML+/fsHtQPeWOF2u6mvr+dHP/oRW7ZsITk5md/+9rckJydfkB0ZRZjGGN/l3KtXr+bOO++kra2NX/ziF3zwwQfY7fZxUeVTFAWXy0V5eTm/+tWv2Lp1KxkZGTz55JNMmTIFnU53QdbQEHPzxiBJkkhISODhhx/2X/Pz2GOPIcsy+fn5mM3mYRlXGYl8XbuWlhaee+45Nm3aRHR0ND/84Q+ZO3fuBd0CVByZxijfDg//7//9Px5++GGcTicrV65k3bp1dHZ2Brp5F4zH46GhoYEf/ehHbNy4kUmTJvHCCy+wcOHC85rEOhAiTGOYLMvodDpuvfVWfvGLXxATE8Pzzz/PY489xqFDh8bcTInu7m727dvHQw89xK5du5g3bx5PP/0006dPH9AlGecroMd6RVHo6OjA4XD4q02+RdP7+/tpb2+nrq7Of3+9Xu+f2Tte1o07X5IkERUVxZVXXklYWBi/+93v+PDDD2lqamL16tVkZ2ef92zpQHM6nZw8eZLt27fzhz/8gYaGBubOnctPfvITsrKyLtrnRVICWDP1eDysWbOG0tJSf7Wpq6uLTz/9lL6+PubMmePfslGSJCZPnsx9991HcHDwBanGjHWKolBaWsqLL77IunXriImJ4a677mLFihWEh4efdnuVkcxXaGhoaOCll17i9ddfx+PxcNddd3HPPfdgtVov7utRAmzbtm3KJZdcopjNZsVsNisGg0HRaDSKSqVSDAaD//akpCTlt7/9reJ0OhWv1xvoZo9afX19SnNzs/KXv/xFyc7OVhISEpRly5Yp+/fvV7q7uwPdvAFzu91KW1ubsmHDBiU3N1exWq1KQUGB8sEHHygdHR2Ky+W66G0K+GXrQUFBdHd3s3v3bv9Gwl6v11+VcTqduFwu5s2bxz333ENMTMyo+vYcadRqtX/niLS0NGw2GwcPHmTbtm309PQQEhKC0Wj076g30vT393Py5En27dvnPxrJssyyZctYvXo106ZNG/aZDQMV0G4efHGoPnjwIHfffTcHDx7E4XCc8nONRoPFYmHDhg3MmTNn1F+aPZIoisLx48fZuHEjzz33HF6vl9TUVO655x7mzp2L2Wz277IXyC8w35dqX18ftbW1rF+/nm3btlFfX09eXh73338/OTk5Q1o4cjgFPEzwxR6i27ZtY/Xq1dTV1Z0y9cVqtfKDH/yAe++9l7CwMHFUGmYejwen00l7ezv/8z//wzvvvENlZSXp6eksXbqUgoICZsyYcVGqYaejfLmFTElJCRs3buSDDz7wbyXzve99j4ULF46YotSICJNveacnnniCv/71r5w8eRL4YmpMXl4eL7zwAvHx8cO2SLtwKkVR/CsDHTlyhI8++oiNGzfS0dFBcHAwEydOZMmSJVx66aVERUVd0EFfr9dLT08PHR0dlJeXs337dkpKSqirq8Nms5GRkcGNN97I3LlzSUhIwGAwjJhK5IgIE3zxJn722Wf89Kc/ZceOHXg8HlJSUvjlL3/JLbfcgiRJAf/mGQ/cbjd2u53i4mJeeeUVioqKaG9vR6/XEx8fz+LFi8nPzycmJobg4GAMBgNarRaNRnPancvPxOPx4Ha7cblcuFwu7HY7nZ2dtLa2UlxczL/+9S8qKiro7e31bxg9f/58VqxYQVJSEmaz+SK8G4MT0DD5vhF9TfB4PLz66qv88Ic/xG638+Mf/5hHH32U4ODgLxr75XrTIlQXR19fH0eOHGHHjh1s2bKFTz/9lM7OTkJCQpg6dSrp6elMmjSJ9PR0EhMTsVqt/t32zvQ3UhTFP75YV1dHTU0NNTU1lJeX+5cottvtBAcHk52dzaWXXkpubi7Z2dnExMRc5HdgcAIWJo/HQ0dHB3/605+ora0F/m8Qt7CwELvdTl5eHlar1X8Yj4yM5K677iIuLu6CzrESvuD1enG73TgcDhwOBx0dHezYsYP33nuPmpoa/+2Kovg3bTYYDISHhxMcHIzZbCYkJMT/d7Xb7djtdrq7uzl58iRutxuv14ssy+j1eoKCgpgyZQqLFy9mzpw5/o3M9Ho9Wq12xHTnziRgYXK73dTV1XHbbbdx6NAh/+2+w7/X60Wj0ZzyBiYlJbF27VqmTp0qzp8C4KvdsePHj3Ps2DGOHz9OQ0MDXV1d9Pb2+meveDwePB4PWq0WSZLo7+/3dwM1Gg1ms5nQ0FBCQ0OJjIwkKSmJ9PR04uLiCA4ORq/Xj7ovzIBGXZZljEbjgPu/RqNxRFRtxivfMIXFYiEpKYkFCxagKAp2ux2bzeY/8jgcDv/4oKIo/vNdtVqNWq1Gp9MRHByMxWLBZDIN66XjgRSwI5Ov79zX1zfgC9d8y9+KQI0svr/lV89/fbd9le9v9tVz37FUWBox1TxBGO1G3nwRQRilRJgEYZiIMAnCMBFhEoRhIsIkCMNEhEkQhokIkyAMk/8PGed1mGTvntcAAAAASUVORK5CYII=)
A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg.
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)
physics-General
physics-
A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.
![](data:image/png;base64,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)
A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.
![](data:image/png;base64,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)
physics-General
physics-
A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N1 and N2 are the normal reactions exerted by inner side and outer side of the tube on the ball
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)
A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N1 and N2 are the normal reactions exerted by inner side and outer side of the tube on the ball
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)
physics-General
physics-
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
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)
According to observer B, the potential energy of the spring increases
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
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)
According to observer B, the potential energy of the spring increases
physics-General
physics-
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
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)
To an observer B, when the block is compressing the spring
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
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)
To an observer B, when the block is compressing the spring
physics-General
physics-
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
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FFixYRUdFN1qpVK0ls+PDhpFKpKDMzkxo2bCiJzZo1i4iI8vLy6I033pDEunTpQllZWURENGfOHEnM3d2d5HI5ERHduHGDGdXc3JxSUlLKvFb6mEeTvLw8On78OE2dOpXatm1bprZamkepVNK1a9eooKBA8rlKpaIbN25QbGxsmccrFAqKjIx8oYyXVWkeb29vdr1WrlwpiXl4eEheizQJDg6WGCsnJ4fFfvnlF8kNqzYdEdGKFSsksQcPHrDYqlWrJLG//vqLxWbOnCmJad7o33//vSR28eJFFktKSpLEZs6cKfk9+vfvz2Jjxowp81q9qHk0Uf8xKY1q1dqWkpKCr7/+Gh4eHvD19WWtQnK5HBMmTICTkxNat24NDw8PdOzYEZcvX5Ycn5aWhnfeeQf16tWDn58fGjdujL59+3KvAG0IoqOjcfPmTQCAs7MzZsyYwWIFBQWSwZvFh+H/9ddfbJuIJFMMimcw3bhxo9ZtAAgJCWHbxZMcrl+/nm0XX6DrxIkTbPuff/6RxC5dusS2jx49KoldvHhRsj9+/Hi2feDAAVQV5S4H+ULW1BNdnzyxsbEUHBxMtWrVkvyFSktLo5iYGHr99de1vqfXqVOHtTZdv369xCuH+ue1117TOUd0VT15vvzyS1bOOXPmSGIHDhwo8buoX7FSUlJKxCZNmsSOrV27tiRWv359Iip6Kqt/N/VPy5Yt2XEtWrSQxGrXrk0qlYqys7MldRYA1Lp1a3acra2tJNakSRMW8/X1lcSMjY1JpVKxuEKhYPUiAHThwoVSr1dFPnnKo1o8eczMzPDTTz9h9erVks/j4uLQo0cPBAUFITo6GgqFAgsWLGDxzMxMLF++HNevX0eXLl3g4eGB06dPQ6lU4sqVKyzL5cOHDzFz5swq/Z14UWfpAVAiJ8CFCxdK6H///XcAwMGDB0vE1DnyUlNTS/TJZGdnQ6VS4d69eyX6gNQZQgGU6B9RKBSIiorCkSNHSvTlxMbGQqlUIjs7G5mZmZLYgwcPWJ9RQkKCJKZSqSRPn1q1asHDw4Ptb926tcTvZgiqhXkaN24Ma2trNG/eXPJ5cHAwtmzZgo8//hheXl6oVasWvvjiC0ybNo1pQkJCMHr0aCxcuBAhISHo3r07TExM4Ofnh+PHj8PExAQAsHv37hL/wS8Dmq9JAwYMKFVnbm4OACyXtLaVuHNzcwEUvf6qb3R1svbc3FwoFApJB6l6RmheXh6Aoj9G6iw5mvnqLl++zEwLAI0aNWLnPHv2LK5cucI6bNVJEVUqFa5du4bMzEykp6cDAOrWrcvOUbxzdPv27Ww7Nja21OtQlVQL86hp3rw5u9mBor9A3bp1K6FbsmQJ0yUnJ+Ojjz7CBx98ACMjI4nOx8eHpUdSKBR49OhRJZZed+Lj4xEWFgag6K/vqFGjJPGoqCi2rc55/ezZM8jlckRERLCYOi9eTEwMe1KoUeccKCwsRHR0tCSDa+PGjQEU1aXkcjlu3brFTKA5dSEqKop9n7m5ORYuXMhiERERku/z8fGRHKd5zlatWmn93QCgbdu2LENP8VhpXLlyBTt27GCJGSuaamUeOzs7yRIcpeUFa9CgAfz8/Nh+WQn42rZty7a1vQYZkm3btrEba8CAAbC1tZXE1Yk1ateujfbt27PP79y5w/5y16tXD76+vgD+ZxDNhByaN+ydO3dw69atUmOax3Xo0IFtR0VFsVcvLy8v9n3qmOZxb7zxBtc5i0/XNjY2ZsZLTk7myk9Qp04dbN68GQ0aNMCAAQOwZcsWliK4InhlJ8OZmZnprNM2fbg01Dd1XFwcZs2apVvhONFsEZswYYIklpeXhwcPHgAousk1/whcvnyZvV75+vqiTZs2rMUsLi5OcmMGBgayV667d+9KYt27d8ehQ4dYLD4+nsV69eqFdevWIT09XfKK5efnB29vb5iYmKCwsBB3796Fg4MDiw8ZMgSLFi0CUPQk1Lz+PXv2xPr165GWllaiBVQul6Np06b4+++/AQBnz56Fi4sL8vLykJeXB4VCwbbVeHh4YNWqVUhNTcWBAwewa9cuzJw5E507d8awYcMQFBQkKZuuvLLmqSqSkpJKNGRUFJ06dYKFhQWeP3+OPn36SGLJycmsYu/u7i6ZxalZJ/D09JTEkpKSWL0IkD4J5HI5i8lkMokhNWPq83p6eiIiIkJSL/P09ISlpSUaNmyI+Ph4yOVyKBQKAICDgwOaN28OGxsb9nqp+TRVn/PixYuQy+WIi4vD0qVLce7cOSiVSkljxVtvvaX1mk2aNKnEZw4ODpgyZQqmTJmCjIwMHDx4EPv27cOcOXPwxhtvYNiwYRg8eLDW5CVlUa1e22oa586dQ3x8PCZMmCBJ5wRAMmLayMhIUp/TbC0rHqNiCwVr9mWoVCoW03bO0r6z+Pdp/lv8nKXFtJ3zl19+wbZt2/DgwYMKW33B1tYWEyZMwOHDh/H48WNMnDgRx48fR5MmTdCtWzesXr0aSUlJXOcST54XpE2bNti5c2elnT89PV3rAlhGRkasQm9jYwNjY2O2b2ZmxratrKxgamrK9gHA3t6e7WseJ5PJ4OTkhJycHFhZWUliFhYWsLa2ZvsFBQVwcHBA48aNoVQqmbnVZqxXrx5UKhXs7e1ha2uL7OxsVl9t2LAh6tSpA0dHx1LPaW5uLulIbdGiBZ4+fcqeqmPHjkWDBg1Qq1Yt9lO7dm3Y2dlh06ZNXNfWxsYGY8eOxdixY5GdnY0//vgD+/btw0cffQRfX18EBwdLWm6LI8yjJ0ZGRiAiWFhYoGnTplX+/UTEKunPnj2DSqVi+wqFgm3n5uZCqVSy/by8PKSlpbF9zeOys7Px5MkTJCQkwNraWhJ7/vw5srKy2H5hYSFSU1ORkJDA6jdqHVD0WpmQkACFQoH8/Hx2TgB49OgRMjMzYWdnB2dnZ0lZ1Oc0MzODv78/a9VbtWoVPvzwQ2aeBQsWaE1Wcv36db2up0wmw8iRIzFy5Ejk5ubi2LFj5TYgCfNUU+rWrcsMnJaWJlnnSPMVR3MFNzWafTTF+7YcHR0RHR2NnJycEkveax6n+Z22trasIzUtLQ2FhYV4+vQpgKL6hvq4nJwcSYW+rHM6ODggLy+Ptf4V/z2KdztUJJaWlhg6dCiGDh1apk7UeaopMpmMdUbGxMRImpg7derEOj9jYmIkdRITExO0aNGC7atb7IrHVCqVpIJe/Lhbt26xmaxeXl7s85iYGGY+oKgRQPOccXFx7Cml7ZxxcXHsOM11TuVyuWTm7MuwqJgwTzVGXYfIzc2V9HvIZDLJyAHNYT3NmzeX9JWpb1agqF6hGdMcpeDu7i6JZWZmMlPKZDL2eW5uruQ4Hx8fyfIjd+7cYc3o7u7ukpjmOS0sLFC/fn0We/ToERvYam1tLcwjeDHUfRTp6emS5mkHBwcWe/TokaSJuVGjRpK+DU3zNGrUSHJTqvtUAKB169aSmGYeaycnJxZLSEiQjGZv27at5DjNNL3e3t6lntPR0VGyQPCtW7dYk7jm08qQVCvz/Pvvv1w9y3l5edwLK1XnxOPqsX5KpRLHjx8HUDQezcPDg8XS0tIkw1lMTU0lYwQ1pymYmppKWvbUUyHMzMzQqlUrSUz9fUCRCdSxhw8fIjQ0lMX8/PwkIxVOnTpVakxzYWRvb2+4uLiwfc0pDZojGAxJtTJPZGSkZOTu9evXS2RzUSgUCAsLYxVWoGjuSHHTqVQqxMbGSm6eq1evIiMjo9osl6g5BEn9KuTt7Q1zc3NJTD1eTSaTsVXI1WP/NEcN+Pr6okOHDqwyrh5I6u/vj9q1a6N+/fpsLJzm08zHx4d1tlpZWbE/SB4eHnBxcZGMZ1PXsYyNjdGpUyc0aNCAPX2Sk5Ml51SPVACkHb+9e/fmuj7Hjh3D+PHjcfDgQdZRW6FU6oSHUtB1Pk94eDjNmjWL3nrrLQoICJD89OzZk/bt20dERHfu3KEBAwaU0AQEBFDnzp3p559/JqKiKcpjx47VqgsICKB58+aVWyZDZM8pTmpqKkum0axZMwJAv/32GxERxcfHk729PQGg8ePHEwCaOnUqO1adFKRTp04EFCURUaOeX6POqLNkyRIWmzRpEgGg6dOnE1CUUEShUNCZM2fY9Gr1XKFPPvmEHTdixAgCQIGBgQSA2rdvz2LqOUvt27cnAOTn50cKhYKIiN566y1JOZ2dnSk/P7/Ua6I5n2fixIm0YsUK8vf3JxsbGxo1ahTt27ePK5EID9XCPC8jL4N5iIjOnDlDFhYW5OXlRePHj5fE9uzZQ2ZmZjRhwgSysrKSTE/Py8sjX19f6ty5MxkZGdHp06dZ7NixY+yctWrVYjkTiIju3btHzs7ONH36dLKzs6Pbt2+z2KBBg6hLly5kYWFBbdq0obS0NBbLyMggNzc3Zp4tW7awmEqlop49e1L79u3Jzs6Obt26xWIRERHk4eHBynno0KEyr0dpk+ESEhLou+++o44dO5K1tTUNGzaMdu3apfMkSE2EefTkZTEPUdFT5sSJE1pj0dHRdObMGXry5EmJWEFBAe3bt09r3rKEhATauXMnPX36tEQsMzOTzpw5ozUZxz///ENHjx4lpVJZIpabm0u7du3SmpVGpVLRkSNHtH5ffn4+7du3j+Li4rT+jprwzCSVy+X0448/UmBgIMlkMgoKCqLt27dTZmZmuefXRJhHT14m8wj+h67TsJOTk2nNmjXUo0cPsrKyov79+9PmzZspPT293GOrVYOBQFDRODs7Y/r06Th16hQePnyIQYMGYefOnWjYsKEk8Yg2xPAcgeC/1K1bF1OnTsXUqVORnp6O8PDwMvXiySMQaMHOzg4DBw4sUyPMIxDoiTCPQKAnwjwCgZ4I8wheWbQld6xIhHkEryyRkZFwdnbG5MmTcfTo0RKT+14UYR7BK0uvXr1w8eJFNG3aFIsXL4aTkxOCg4Nx6NChChkoKswjeKXx9PTEggULcOXKFURGRsLb2xvLli2Dk5MTxowZg5CQEDZ6XFeEeQQ1Bnd3d3zwwQeIiIjAzZs30a5dO6xcuRLOzs4YMWIE9uzZw6Z28CDMI6iRuLq6Yu7cuTh//jzu3LmDzp07Y/Xq1ahXrx6GDh2KnTt3lpvjWphHUONxcXHB7NmzERYWhtjYWPTs2RMbN26U5P/WhhjbJhBoUK9ePcyYMQMzZswQTx6BQF9sbGzKjBv8yfPo0aNKTVdbWRARy4ApqJmYaqYCqio0Vx+7c+cOxowZU+VlqAhcXV2RkZEBQ1xDgXY0U2lVNqY9evSosi/Thi5Ngy8b6pROhr6GAu1UdhYkg7+2CQQVibGxMZydnVFYWFgiLVlFY2pvb691vU5t3LhxA+Hh4dwrR589exYJCQkYN24cl/7w4cMwMTEpdeGi4mzfvh3u7u4ICAjg0v/www/o0aOH1uz6xVGpVPjiiy8wceJErrVhFAoFli1bhvnz50vSz5bGkydP8PPPP2PRokUl1t7RRkxMDA4dOoR58+Zx/V9dvnwZN2/exOTJk8vVAkXJCJ89e4YhQ4Zw6ffs2QMHBwfup+6GDRvw+uuvSxbMKotvvvkGQ4YMYeuploVSqcSyZcswa9YsODg4gIiQmpqKXr16cX2X3nz88cfcyRWGDh1K3333Hbe+ffv2tHfvXi6tSqWihg0b0pUrV7j02dnZJJPJKCkpiUt/7949srGxYfnAyiM0NJSaNGnCpSUi2rp1K/Xs2ZNbv2TJEpo4cSK3fvLkybRo0SJufe/evWnTpk3c+pYtW0rST5WFQqGgOnXq0N27d7n0//77L1lYWHAl1SAqSuLRoEEDKiws5NIfOXKE2rZty6WtSMB7AbKyssjKyooePXrEpb9//z7JZDLuBHPh4eHk4eHBpSUi2rlzJ3Xr1o1b//nnn5fIa1YW06dPpwULFnDr+/XrRxs2bODWt2jRgo4dO8alzcvLI1tbW7p58yaX/smTJ2Rpacl9s0ZFRZGzs7PWdFHaOHjwIPn6+tuoS54AAAdwSURBVHJpiYhWr15N/fv359YvWLCA5syZw60fP348rVixgltfUXCnnvrtt990SrP01Vdf0ahRo7j1s2bN0ulmDQoKorVr13Lrvb296ciRI1xapVJJjo6OdO3aNS59WloaWVpaUmpqKpc+KiqKHBwcysx8qckff/xBLVq04NISEa1bt06nm3Xx4sX07rvvcuvHjBlDX3zxBbe+S5cutHXrVm69u7s7XbhwgUurfgrGx8dzn7+i4DZPUFAQ/fjjj9wn9vPzo/3793NpCwsLqX79+nT16lUu/bNnz0gmk2lNkKeN27dvk62tLffNeuLECWrWrBmXlojo119/pb59+3LrFy9eTNOmTePWBwcH09KlS7n13bt31+lmbdasGYWFhXFpnz9/TtbW1lwJCImKEgxaWFhwJxS8fPkyNW7cmFQqFZd+//791KFDBy5tRcNlnmfPnpGVlVWl1i88PT25tERE27Zto169enHrlyxZQpMmTeLWT506lRYvXsytf/PNN7nrFyqVipo1a0YnT57k0j9//pxsbGy0ZtnURnJyMllYWFBGRgaXXtf6xe+//65T/WLVqlU6Jbb84IMPuHKFqxk9erRO9fCKhMs827dvp65du3Kf9PPPP6dx48Zx66dPn65TZbh///60ceNGbn3z5s3p+PHjXNr8/Hyyt7enqKgoLv3Tp091ql9cv36dHB0dqaCggEt/8OBBat26NZeWqKh+MXDgQG79ggULuDJrqhkxYgQtX76cWx8QEMCSz/Pg6upKly5d4tLm5uaStbU1dz28ouEyz4ABA2jNmjXcJ23dujUdPnyYS6tUKsnJyYlu3LjBpU9PTycrKyvu+sWNGzfIwcGB+2Y9evSoTvWL9evX04ABA7j1CxcupBkzZnDrx4wZQ8uWLePWd+nShXbs2MGtb9KkCZ0/f55Lm5OTQ1ZWVvTw4UMufUJCAllaWlJWVhaX/u+//yY3NzcuLRHR3r17DZruuFzzZGRkkKWlpdZE4dqIjo4mW1tbysvL49KfPHmSmjdvzqUlItq0aZNO9YtFixbpVL+YOHGiTvWLHj160LZt27i0KpWKPDw8KDQ0lEufm5tLMpmM7t27x6WXy+VkaWlJz54949L/888/1KhRI+76xe7du8nf359LS0S0cuVKGjp0KLd+7ty5NH/+fG798OHDdaqHVzTlmmfLli069V8sXbpUp/6LadOmkS59TX379qXNmzdz65s2bUqnTp3i0qqbhO/cucOlT05OJisrK+7KcGRkJNWrV4+7Sfj3338nPz8/Li1RUf1i8ODB3PoPP/yQ3n//fW79kCFD6Ntvv+XWt2/fnvbs2cOlVffzRUZGcul17eerDMo1T2X2XxQUFJCDg4NkPZaySE1NJSsrK+7KcGRkJDk5OXHfrIcOHdKpfvHzzz/rdLN+9NFHNHv2bG79iBEj6Ouvv+bWBwQE0M6dO7n1r732GkVERHBps7KyyNLSUrJWT1k8ePCAZDIZ5eTkcOnDw8OpadOmXFqion4+XerhlUGZ5klPT9ep/+LmzZtkb2/PXb84duwYtWzZkktLRLRhwwad6hcfffSRTvWLcePG6VS/CAwM5L5ZVSoVubm5UXh4OJc+OzubrKystK6dow1d6xcXL16k1157jUtLRLRjxw7J6nHl8fXXX9PIkSO59bNnz6aFCxdy6wcPHqxTPbwyKNM8v/76K/Xp04f7ZIsXL5Ys3VcekyZN0ql+0atXL9q+fTu33s3Njf766y8urbpJWHP1tLKQy+Ukk8m4b9bLly+Ti4sLd5Pw7t27JUsPlsfKlStp2LBh3Pr333+fPvzwQ279wIED6YcffuDW+/n5UUhICJdW3c/H22ik7ufjrYdXFmWap0+fPjqNj/L09OTuv1DXL3j7L548eUIymYy7Mnzp0iWqX78+980aEhJCbdq04dISFdUvhg8fzq3/4IMPaO7cudz6IUOG0MqVK7n1+tQveMcRZmRkkIWFBT1+/JhLr+7ne/78OZc+NDRUp0YjXfv5KotSzaOuX/D2X1y9epUcHR256xeHDx8mb29vvlIS0Zo1a3SqX8ybN0+n+sXIkSN1ql907NiRLSRcHiqVilxdXenixYtc+mfPnpGFhQUlJCRw6R88eEBWVlbc62ueO3dOp3GEmzdvpsDAQG79559/TmPHjuXWT58+XbL4b3n0799fp3p4ZVGqeXJycrhfYYiK6ke6jC96+vQpyeVybv3jx4+5h+MQET18+JC7YYGIKDY2VqfFXW/fvs3dHK9UKunWrVvcTcK5ubncLX5ERWuE8g6XISoai6dLx2JycjIlJydz6xMTE7nryURF5ud9/SUiiomJ4X6qVSZGRESVO+lBIHg1EdlzBAI9EeYRCPREmEcg0BNhHoFAT4R5BAI9EeYRCPREmEcg0BNhHoFAT4R5BAI9EeYRCPREmEcg0BNhHoFAT4R5BAI9EeYRCPREmEcg0BNhHoFAT4R5BAI9EeYRCPREmEcg0BNhHoFAT4R5BAI9EeYRCPREmEcg0BNhHoFAT4R5BAI9+X+xkYwKILZNrwAAAABJRU5ErkJggg==)
According to the observer A
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
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)
According to the observer A
physics-General
physics-
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
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)
To an observer A, the net work done on the block is
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
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)
To an observer A, the net work done on the block is
physics-General
physics-
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
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)
To an observer A, the work done by the normal reaction N between the block and the spring on the block is
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
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)
To an observer A, the work done by the normal reaction N between the block and the spring on the block is
physics-General
physics-
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
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)
To an observer A, the work done by spring force is
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
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)
To an observer A, the work done by spring force is
physics-General
physics-
A 1.0 kg block collides with a horizontal weightless spring of force constant 2.75
as shown in figure. The block compresses the spring 4.0 m from the rest position. If the coefficient of kinetic friction between the block and horizontal surface is 0.25, the speed of the block at the instant of collision is
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)
A 1.0 kg block collides with a horizontal weightless spring of force constant 2.75
as shown in figure. The block compresses the spring 4.0 m from the rest position. If the coefficient of kinetic friction between the block and horizontal surface is 0.25, the speed of the block at the instant of collision is
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BwcOCCzdfXF0lJSRRshBAAahi53b9/Hx4eHtwS5A0aNEBYWBi+++47peplZGRg7NixSE1NBfB28vzWrVuVuv2EEMK/CRMm4Ouvv4aTk5NKHrZcXSoduW3evBkWFhZcsNnY2CA1NVXpYIuIiEDPnj25YBs6dCiuX79OwUbIB2T8+PGIjY2FhYUFHBwcsHbtWm5VIHVSycgtOzsbEydOxPHjxwEAOjo6CA0NxaxZsyAUKp6nf//9N7y8vHDq1CkAb+esrlixAr6+vrz2TQipOXt7e4wZMwalpaW4fPkyoqKiMHDgQDRr1gwuLi5wcXGBqampyvvgPdwOHz4MHx8fbtlgCwsL7N69G+bm5krVO3bsGCZOnIicnBwAQI8ePbBnzx61fDiEEOWJRCIMHDgQAwcOxIoVK5CamorDhw9j1KhRkEqlcHFxwYgRI9C7d+8P/1aQixcvws3NDbm5uRAKhQgKCkJ8fLxSwfb69Wv4+PjA2dkZOTk5EAqFmDNnDq5evUrBRkgtIxAIYGlpiZCQEFy/fh3Hjh1D48aNMWPGDLRv3x4bNmzgfZ+8rgpSdt9ax44dsWPHDgwYMECpegkJCRg3bhy34q6BgQF27txJy4gToiU6deqE2bNnY/bs2Xj8+DEePHjA+z54XxXE29sbKSkpSgWbTCbD4sWL0b9/fy7YxowZg9TUVIWDrbCwUCXz1Qgh/GrTpo3SA6F34fWc24gRI/DLL78o9d6HDx9i/PjxuHjxIoC3887WrVuHsWPHKlwrNTUVY8eORUZGhlK9kHd7/vw5Tpw4gcTERMTHx+PNmzeoV68ezMzMYGdnBzc3N4Wej1FaWoro6Ghcu3YNV65cQXZ2NgQCATp06IAePXrA09MTrVq1qna9nJwcnDx5EomJiUhISOD669q1KxwcHDBixAiFHiH59OlT/Prrrzhz5gwaNmyI5ORk6OrqonXr1jA3N8f48eNhZmZW7XpETRgPLC0tGQDm6emp1Pt3797NGjVqxAAwAGzQoEHswYMHCteRyWRsxYoVrE6dOlytsq+tW7cq1Rv5//Ly8lhwcHCln+9/v/73v/+x/Pz8d9bLz89nu3fvZsbGxu+tN27cOHbr1q131svNzWXTpk1jEonknbUEAgELDw9nBQUFVdaSyWQsICCANW/eXO691tbWldZ0cHBgqampSn2u2mDfvn3cZ5Gdna3pdhhjjGk03F6+fMnGjBnDfSgSiYQtXryYlZaWKtzDkydP2GeffcbV0tXVZWvWrKFw48mtW7dY165dmVAo5D7TwYMHs/nz57PQ0FA2f/58Nnr0aFavXj3udX19fXbq1Kkq6wkEArmAMDIyYjNmzGChoaEsJCSETZo0iVlYWMht8/3337OioqIK9a5fv850dXUrBM6CBQtYaGgomzdvHhs1ahTT0dHhXm/VqhWLjo6uUEsqlbJhw4ZVCLBu3bqxKVOmsJkzZzIvLy/Wv39/uc9j4MCBLCAggBUWFvL++X/oKNzKOX/+PDMwMOA+EBMTE5aQkKDU/o8cOcKaNWvG1erVqxe7c+cOy8vLo3DjwZ07d1ijRo2YUChkQqGQtWzZkiUmJla6rVQqZevXr5cLBS8vL/by5Utum7179zKRSCS3zfLly5lMJqu0ZlJSEuvQoQM36urUqROLj4/nXj958qRcvbp161Y5iiopKWGrV6+W2/d3333H8vLyuG1Gjx5dIdSq+vNev36djRs3jpmZmbG6desyAMzU1JRdu3btvZ+rNikfbpGRkezNmzeabkn94VZcXMyCgoLk/sWbNGnSOw8RqlJQUMB8fHy4OkKhkM2ZM4cVFxczxhiFG0/s7e0ZACYSiZiZmRnLycl573v2798vNyI3NjZm2dnZ7MCBA3LBIRKJ2MmTJ99b78mTJ6xVq1ZMKBQykUjERCIRO3LkCHv+/LncYWirVq3Ys2fP3ltv586dcv116dKF5eTkVAi+DRs2VOszevToEXNycuLeJxaLWXh4eLXeqw3Kh5ujoyNr1aoVc3d3Z4cOHXrv6QlVUWu43bx5k/Xo0YP7EJo3b86OHTum1D6TkpKYqakpV6tt27bsjz/+kNuGwq3mXr16xZo2bcoAsAEDBrDnz59X+73z58/nRlQSiUTuHzShUMhatGhR4e/sXVJSUuQOK/97WGtjY8NevHhR7XqBgYFV9lenTh22cuXKatcqs3PnTtakSRO5c4X//POPwnVqm/8elr569YodPHiQjR07lrVs2ZI5OzuzHTt2KPTzU1NqC7d169ax+vXrcx/AkCFD2N9//63wvmQyGVu+fLncD/moUaMq/QGicKu5gIAA7jPcv3+/Qu8tLS1lQ4YM4UZWZeGhp6enUAiVFxkZWekJ/RMnTihcSyqVMnt7e66/sqBr2rSpUkcSZR48eMD9I965c2c2duxYpWvVFu865/bmzRt26tQp5u3tzdq2bcvs7e3Z2rVr2ePHj1Xak8rDLTs7W264Xq9ePbZmzRql9vPo0SPuEAkAa9CgwTtDi8JNOUVFRWz79u0sKiqKGx25uroqVevx48cVDkP19fUrvShQXX379q0QbpcuXVKq1oMHD+TqiMVi1rZtW+7UhjL279/PsrKymLu7OzMyMmJCoZAdOnRI6Xq1QXUvKEilUhYbG8sCAgJYx44dmbW1NVu6dCnLzMzkvSeVhtvx48dZixYtuD+0lZUVy8jIUGofhw8f5g6PALA+ffqwe/fuvfM9FG7KycvLY23atGENGzbkzmM9efJEqVrnz5+vEERisZgFBwcr3Vv524bKRoSGhobs9evXCtc7e/Zspf0tXLhQqf4YY8zOzo5FRUWx58+fcz//zZo1q1Ggf+iUuVoqk8lYSkoK++GHH1hISAjvPakk3F6/fs0mT54s98M3e/Zspa6g5Ofns4kTJ8rVmjt3LispKXnveynclDdy5EjuF/3ixYtK1cjKyqoQROXPlyUnJytUTyaTMTc3NyYWiyucb5NIJGzWrFkK1bt//z5r0KBBpf2JRCKWnp6uUL3yfZZJS0vj7gv85ZdflKpXG3wUt4IkJSWxLl26cH/Qdu3aKXTSuLz4+HjWuXNnrpaBgQG7cOFCtd9P4aacjIwM7vzY8uXLlapRXFzMevXqxcRiMROLxVxQlh8d9evXr8rbPyqzevVqJhQKmUAgqPRGYpFIxO7evVutWkVFRczCwoKJRCKur/JXXcViMbOzs1Oov6rMnj2bAWCffPKJ0kcuHzqtD7eePXvKnej/+uuvlTpxXFpaypYsWSL3w/bVV18pXIvCTXEymYwNHTqUAW+vjir7yx0UFMSFRrt27VhmZmaF0RYAdvbs2WrVS05OlruX7dy5c8zGxkaupkQiqfbJ+5kzZ3IjwA4dOrCMjIxKR3CK/GNalaysLK7e1KlTa1zvQ/Qhhhsvc0uLi4sBAImJiQAAPT09rF27Fu7u7grXevToEcaPH4/z588DABo2bIg1a9bAw8NDqVofgxMnTmDFihW81MrNzcX169cBANOnT1dqna3U1FQsX76cWy0mIiICRkZGcHBwQHR0NPd9sViMTZs2vfepZzKZDOPHjwdjDBKJBF9++SUGDx6M7OxsXL58matXUlKCAwcOYP369dDT06uyXnx8PFauXMn9/9q1a9GlSxcMGDAAly5d4r4vkUiwefNmDBw4UOHPoLy2bdvC3NycW+rH2dlZJeuXadKtW7c03UJFfCRk+UNHGxsbdv/+faXqHDhwQO4eob59+7I///xTqVrbt29nenp6H8XI7Zdffql01FGTrwYNGrDc3Fyl+hkyZAgTi8VMIpGwQYMGcaO/sLCwCoeTEonkvfeBHTp0iBuhicVi7spaTk5OpRcDNm7c+M569vb2TCQSMYlEwhwdHbnvL1mypEJ/derUkZu9oKzLly/z/nf0IX2V/11T5hYvVeBl5Fa/fn0AgJWVFc6fPw+RSKTQ+/Pz8zF9+nRs27YNwNsVPIODg7FgwQKIxYq1mJOTA29vbxw5ckSh99VmhoaGcHZ25rXmoEGD8Mknnyj8vvT0dJw8eZL7/+XLl3OjFGtra7x586bCew4cOABvb+8qay5YsADA2+XqfX19YWRkBABo1qwZWrdujSdPnnDbSqVSbNq0qcrndCQmJuLcuXMA3q5GEhYWxr3Wp0+fCv2VlpYiKipKqSOH8vr164fvv/8eS5YsqVGd2sDa2hpubm5wdXVFv379lHq0AB94XfLIwsJC4WC7du0axo0bh3v37gF4+4u6e/dupdZ3OnLkCHx8fPDs2TMAQIcOHbgFNLXZ559/js8//1zTbQAA9u3bBx0dHRQXF6Np06bo06cP95qVlRWEQiFkMhn3PZlMhuTk5Crr3blzBzdu3ADw9vSHi4uL3Ot9+/ZFVFQUd2gKANevXwdjrNJDv/L9tWvXTm6posoeCykQCJCcnFzjcAOA0NBQjBs3rsZ1PkSnT59GQEAAAODgwYOIjY1FcHAw7t27BycnJ7i6usLOzk6hpbBqjI/hnzIT50tLS9lPP/0kdwVt7NixchOsq+vly5fMw8NDbpjs6+vLnj59+lEcln5IzMzMGACmo6PDpk+fXuF1IyOjCoc0w4YNq7JeeHg4d5GqWbNmFW4B+umnnyq9cvrq1atK65VNwNfR0WFz586t8Hr5+zLLvkaPHq3gp/DxqeqCwrNnz9iWLVuYk5MTa9GiBRs7diw7cOBAlX8/fNLIePGvv/6CnZ0d5s2bB6lUCj09PezevRt79uxBo0aNFKp17tw5mJubY+fOnQDerup5+vRprFu3Drq6uqpon1ThxYsX3AKhxcXFmDZtWoVtunXrVuF77xrtnz17FiUlJdDR0cHkyZMrnKYwMzNDSUlJhfdVdij07NkzbiRfXFyMSZMmVas/TR1WaYPmzZvjm2++wW+//Ya7d+9ixIgROHz4MIyNjeHs7Izt27fj+fPnKtm32v/WIiMj0b17d1y4cAEA0L9/f6Smpio8XC8sLMS0adPw2WefISsrCwAwbtw4pKenfzCHaB+bhw8fcv/duHFjGBsbV9ima9eucqvgSiQStG/fvsqat2/fBmMMJSUllZ6qMDY2ljvMBd4++LvsPHB59+/f5/5bX18fbdu2rbCNmZmZXIDq6Oi8sz9SfQ0bNsSoUaOwd+9e/PXXX5g8eTKuXr0KS0tLzJ8/n/f9qfyJ82VevXqFqVOnciMskUiE+fPnY968eQqfp4uLi4Onpydu374N4O2J5Q0bNsDNzY33vkn1ZWRkQCwWQyqVonXr1pVu06lTJ7nzYyKRqMptpVIp9+AQxhjatWtXYZvKLnq0aNGiyv4kEglKSkoqrVVWTyQSQSqVAng7aquqP6I8HR0dODo6wtHRETKZTO6iEF/UEm5Xr17FuHHjuEMCIyMj7NmzB/369VOoTklJCRYuXIilS5eitLQUADBs2DBs2rSpyh9ooj55eXlcMFR1KGdkZMQFR5mqti0uLub+nqvarrKLBlXVK+uvpKSkym3+W48xRoelKiYUCisdRde4Lu8VyyktLUVISAgGDhzIBZu7uztSUlIUDrb09HT06dMHixYtQmlpKRo2bIgtW7bg2LFjFGy1yH/Pg5aWlqJ58+a87oPPnwepVIpmzZrxVo+oj8pGbg8fPoS7uztiY2MBvH2a1fr16zFmzBiF6shkMvz8889YsGABdw/Sp59+iu3bt9O5kA9Yeno6ZDJZhVHPy5cv5f6/pKQElpaW1ar5+vXr926jo6OD3r17V/l62SFxfHx8tfZZWlpa7f7Ih0UlI7e9e/eie/fuXLDZ2NggNTVV4WDLzMyEra0tgoKC8ObNG9StWxfh4eGIiYmhYPsAmZqayt0EW9mDdm/evCl3QaFly5awsLCotF69evXkRmGpqakVtvnvldLi4mKMGDGiyv7KpgoCwL///vveeu3bt4eJiUml9ciHjddwKy4uhru7O8aNG4d///0XYrEYoaGhOH/+vMJh9Msvv8gFZK9evZCUlISZM2dq3bw8bTFo0CCYmOXGNb0AAAuxSURBVJhAKBSiXr16CAwMrLBNXFwcd85NLBZj1qxZVf59CgQCBAQEcFcvQ0JCUFBQILfNzZs3ufeLRCJ07doVNjY2ldZzcHCAoaEhBAIBxGKx3PzSMtevX+cCWiQSITAwkH7eFLRx40b89ddfmm6D35t4yz9arWPHjuzq1asK13r8+DH74osv5OYKLly4sFrrt/0XrQqifhkZGaxx48YMeLtm27Jly7hHNRYVFXHPARWLxaxbt27vXfH2zZs3bNiwYdzSSf3795eb6zljxgzuJl+RSPTep06lpaXJzYNcv34991pBQQH3mkQiYT169GBSqbQGn8bHo/xNvNOmTWMmJiasR48eLDQ0lF2/fl0jPfESbmV3fZd9eXp6KjXZeO/evXIT583MzJR+3B9jFG6aEhMTw0QiERMIBEwgEDBDQ0M2fvx4ZmJiwsRiMRMKhaxRo0bVfvB2fn4+MzU1ZWKxmIlEItakSRPm6uoqt3z9f4PqXU6fPs2tCweAmZubMw8PD2ZsbMz117RpU5aVlVWTj+GjUtkMhRs3brCffvqJ9ezZk3Xq1IkFBgayy5cv87JGXnXwEm5lD86VSCQsMjJS4ffn5ubKPStSKBQyf3//Gj/c9sWLFxRuGpKYmMj9XJRfh00sFrNGjRop/HT2vLw8bkXm8vXKFtVcunSpQvXi4uK4RVX/21+TJk20dlFJVXnfem4PHjxgK1euZLa2tqxt27bMx8eHnTp1qkbPqngfAWPl7qhUkpWVFVJSUuDm5oaDBw8q9N4TJ05g4sSJ+PvvvwG8nTi/fft22Nra1qinpKQkfPPNN9xJ6K1bt8LLy6tGNYliGGM4c+YMLl68iAcPHoAxBgMDA3zzzTfo1KmTUjX//PNPREVFISMjA2/evIGuri6cnJwwfPhwpfr7/fffcenSJe7ih6GhIb799lt06NBBqf4+Vvv37+cuGGZnZ0NfX7/KbXNycnDs2DFERUUhISEB9vb28Pb2rvHvfAV8JKQyE+fL/0tc9vXtt9/WeO2sgoICFhAQUOGJ5jRyI0R1lF2JNy8vj0VGRrItW7bw3pPapl+Vd+HCBUyYMIGb69eyZUts2rQJTk5ONap75swZTJo0iaurq6tb4eoaIeTD0bBhQ4wePVoltdU6r6SoqAgBAQGws7PjAmjUqFFIT0+vUbDl5OTA3d0djo6OXN1hw4ZV+0ZNQoj2UdvILTExER4eHtySOE2aNMHatWsVvrH3v3bu3Al/f39u2ZSWLVti9erVGDVqFF69elXjvgkhtZPKR25SqRQLFy5E3759uWBzdHREenp6jYItMzMTn332GTw9PfH8+XMIBAJMnDgRN2/exKhRo/hqnxBSS6k03G7duoV+/frhxx9/hFQqha6uLtavX49Tp04pvYyMVCrF8uXL0a1bN0RHRwMATExM8Mcff2DTpk1o3Lgxn38EQoiC8vPzNd0CABWFG2MMK1euhJWVFRISEgAAAwYMQGpqaqWrn1ZXQkICevfujaCgIBQWFkIikWDevHlITU3l/zIyIUQp/fv3x9ChQ7F582bk5ORorA/ew+3hw4cYPHgw/Pz8UFRUhDp16mDZsmW4cOECOnbsqFTNgoIC+Pv7o2/fvkhJSQHw9mlCycnJCA0NRZ06dfj8IxBCaiA5ORmzZs1CWloa+vTpA1tbW6xcuVLt8015vaBw9+5dWFhYIC8vDwDQvXt37Nq1C+bm5krXPHXqFHx9fbmbLBs2bIglS5bA19eXFhEk5AMkEolgZ2cHOzs7rFq1CgkJCYiKioKjoyPq168PFxcXuLi4oGvXrirtg5d0KFsm5vLly9xqp8HBwYiPj1c62J49e4axY8fiyy+/5ILN2dkZGRkZmDJlCgUbIbWAQCBA7969sXjxYty8eRN79uyBUCjEhAkTYGpqijlz5iAuLk5u6Xm+1DghGGNyzwbt3LkzYmNjsWjRIrl1uxSxbds2dOnSBfv27QMAtGrVCgcPHsSRI0dUshwxIUQ9TE1NuYHP2bNn0aZNG8yZMweTJ0/mfV81PiwVCARo06YN7t27B1NTUyQmJlb65KHquHfvHnx8fBATE8PV9vb2xrJlyxR+5B8h5MPWrl07TJs2DdOmTavwXA0+8HJs16BBAwCAtbW1UsEmlUqxdOlSWFhYcMFmamqK//u//8OGDRso2AjRcv99Hi0vNXmvqKBr167hu+++Q1paGoC3a+DPmTMHwcHBdBWUEKI0jYVbfn4+5s2bh4iICO6huv3798emTZtgZmbGyz7++7BeQsjHQyOXHE+cOIGuXbti1apVkMlk0NPTw7p16xAbG8tbsMXFxcHOzo6XWoSQ2ket4ZadnY2vv/4aTk5O3A19I0aMQEZGBnx9fXl5EEd2dja8vLy4m3zL0CiOEPWYOXMmjh8/LvckNE1QW7ht2bIFXbp0QWRkJACgdevWOHz4MKKiotCmTZsa15dKpQgPD4eJiQm2b98Oxpjcw3TpvjhC1MPW1ha7du2CkZERRo8ejf3793M39quTyn/j7969Czs7O0ycOBEvXryAQCDApEmTkJGRARcXF172ce7cOXTv3h3+/v7cIwVnzJghN3IjhKiHi4sLIiMjkZmZCQ8PD5w9exZmZmYYMmQINm3ahGfPnqmlD5WFW0lJCRYvXgwLCwucP38eANClSxdcvHgR69ev5+X2jocPH2LkyJFwcHDgllOys7NDSkoKVq5cSbeQEKJBdevWhZOTE7Zs2YKHDx9i9uzZSE9Ph7W1NQYNGoTw8PBKH9zNF5WEW1xcHHr27Im5c+eiqKgIOjo6+PHHH5GSkoIBAwbUuH5RUREWLlyILl264NChQwDe3hD466+/IiYmRuVz1gghihGJRPj000+xatUq3L9/H2FhYcjNzcWQIUPQo0cPbjYSn3i9FaSkpATTp0/H2rVruRP4NjY22LRpE0xNTXnZR1RUFPz9/bnEr1OnDgIDA/H9998rPTOCEKJevXr1Qq9evbBo0SLcvn0bWVlZvO+D13A7cuQIXr9+DQBo1KgRli1bBm9vb16ugt66dQvTp0/H2bNnue8NHz4c4eHh9Bg2QmoxExMTmJiY8F63xuHGGONGUWXB5urqioiICKVX2y3v1atXWLhwIVavXs2tPmJiYoKVK1fiiy++qHF9Qoh24mXifL169fDy5UvUr18fe/fuhbOzc40bY4xh165dCAoK4h7Y3LBhQ8yfPx8zZ85UesURQsjHgZfDUn19fTx9+hTOzs68BFtSUhKmTp2KK1eucN9zd3fH8uXL0apVqxrXJ4RoP16ulpadU9PR0alRndzcXPj4+KB3795csFlZWSE2Nha7du2iYCOkFihbBEPTPojb9ktLS7F27Vp07twZGzduhEwmQ9OmTbF+/XokJCTwcvsIIUQ9AgMDYWxsjKCgII0+GF3j4XbhwgX06NEDU6dOxYsXLyASieDr64u7d+9i0qRJNG2KkFrm9OnTiImJQcuWLeHn54cOHTogICAAV65cUcly4lXh9VaQp0+f4o8//qjWtjk5OdiwYYPc9t26dcP06dNhbGyM1NTUGvdTdvW2pofLhBDFGBgYwM/PD35+fnj69CkOHz6MuXPnIjMzE87Ozhg5ciQGDBig0sGLIDg4uMZRum3bNjx79gw6OjooLCzkoy9eNW7cGAMGDED37t013QohWunGjRs4evQogLcr8+jr61e6XU5ODo4cOYJDhw7hzz//5ILO2tqal/thyxMAUN84kRCi9d4Vbuokbt68eY2LKPJwB8YYCgoKwBhD/fr1IRKJarz/6hAKhXT+jhAVKSoqwqtXrzTdhhyxupYfKa+4uJjOgxGiRTIzM3Hu3DkAgJ6enoa7eUvA1Hn5ghBC1ISO0wghWonCjRCilSjcCCFaicKNEKKVKNwIIVqJwo0QopUo3AghWonCjRCilSjcCCFaicKNEKKVKNwIIVqJwo0QopUo3AghWonCjRCilSjcCCFaicKNEKKVKNwIIVrp/wFWAEmZ71hW8AAAAABJRU5ErkJggg==)
physics-General