Physics-
General
Easy
Question
A rod of mass m and length 1 is hinged at one of its end A as shown in fig. A force F is applied at a distance x from A. The acceleration of centre of mass (A) varies with x as
"![](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/answer/887600/1/4118706/Picture39.png)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/answer/887600/1/4118707/Picture40.png)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/answer/887600/1/4118708/Picture41.png)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/answer/887600/1/4118709/Picture42.png)
The correct answer is: ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/answer/887600/1/4118707/Picture40.png)
Related Questions to study
physics-
A uniform wheel of moment of inertia 1 as shown is pivoted on a horizontal axis through its centre so that its plane is vertical. A small mass m is stuck on the rim of the wheel as shown. The angular acceleration of the wheel when mass is at point A is
and when mass is at point B is
. Then
![](data:image/png;base64,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)
A uniform wheel of moment of inertia 1 as shown is pivoted on a horizontal axis through its centre so that its plane is vertical. A small mass m is stuck on the rim of the wheel as shown. The angular acceleration of the wheel when mass is at point A is
and when mass is at point B is
. Then
![](data:image/png;base64,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)
physics-General
physics-
A rod AB of length 1 m is placed at the edge of a smooth table as shown in fig. It is hit horizontally at point B. If the displacement of centre of mass in 1 s is
. The angular velocity of the rod is ![left parenthesis g equals 10 blank m divided by s to the power of 2 end exponent right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
A rod AB of length 1 m is placed at the edge of a smooth table as shown in fig. It is hit horizontally at point B. If the displacement of centre of mass in 1 s is
. The angular velocity of the rod is ![left parenthesis g equals 10 blank m divided by s to the power of 2 end exponent right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
A uniform rod of mass m, length l is placed over a smooth horizontal surface along y-axis and is at rest as shown in figure. An impulsive force F is applied for a small time
along at point A. The x-coordinate of end A of the rod when the rod becomes parallel to x-axis for the first time is (initially the coordinate of centre of mass of the rod is (0,0)) :
![](data:image/png;base64,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)
A uniform rod of mass m, length l is placed over a smooth horizontal surface along y-axis and is at rest as shown in figure. An impulsive force F is applied for a small time
along at point A. The x-coordinate of end A of the rod when the rod becomes parallel to x-axis for the first time is (initially the coordinate of centre of mass of the rod is (0,0)) :
![](data:image/png;base64,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)
physics-General
physics-
Moment of inertia of a triangle plane of mass M shown in the figure, about vertical axis AB is:
![](data:image/png;base64,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)
Moment of inertia of a triangle plane of mass M shown in the figure, about vertical axis AB is:
![](data:image/png;base64,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)
physics-General
physics-
The radius of gyration of solid hemisphere of mass M and radius R about an axis parallel to the diameter at a distance 3/4R from this plane is given by ( centre of mass of the hemisphere of the hemisphere lies at a height 3R/8 from the base)
![](data:image/png;base64,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)
The radius of gyration of solid hemisphere of mass M and radius R about an axis parallel to the diameter at a distance 3/4R from this plane is given by ( centre of mass of the hemisphere of the hemisphere lies at a height 3R/8 from the base)
![](data:image/png;base64,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)
physics-General
physics-
A square plate of mass M and edge L is shown in fig. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° from horizontal is
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)
A square plate of mass M and edge L is shown in fig. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° from horizontal is
![](data:image/png;base64,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)
physics-General
physics-
A circular plate of radius 1/2R is cut from one edge of a thin circular plate of radius R. The moment of inertia of the remaining portion about an axis through O perpendicular to plane of the plate (i.e about the
axis
is ( M= mass of remaining circular plate. )
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)
A circular plate of radius 1/2R is cut from one edge of a thin circular plate of radius R. The moment of inertia of the remaining portion about an axis through O perpendicular to plane of the plate (i.e about the
axis
is ( M= mass of remaining circular plate. )
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)
physics-General
physics-
A symmetrical lamina of mass M consists of a square shape with a semicircular section over each of the edge of the square as shown. The moment of inertia of the lamina about an axis through the centre of mass and perpendicular to the plane is
. The moment of inertia about the tangent
in the plane of the lamina is
![](data:image/png;base64,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)
A symmetrical lamina of mass M consists of a square shape with a semicircular section over each of the edge of the square as shown. The moment of inertia of the lamina about an axis through the centre of mass and perpendicular to the plane is
. The moment of inertia about the tangent
in the plane of the lamina is
![](data:image/png;base64,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)
physics-General
physics-
A uniform disc of radius R lies in x-y plane with its centre at origin. Its moment of inertia about the axis x= 2R and y=0 is equal to the moment of inertia about the axis y=d and z=0. Where d is equal to
![](data:image/png;base64,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)
A uniform disc of radius R lies in x-y plane with its centre at origin. Its moment of inertia about the axis x= 2R and y=0 is equal to the moment of inertia about the axis y=d and z=0. Where d is equal to
![](data:image/png;base64,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)
physics-General
chemistry-
Ionisation energies of Ni and Pt in kJ mol–1 are given below
![](data:image/png;base64,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)
Ionisation energies of Ni and Pt in kJ mol–1 are given below
![](data:image/png;base64,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)
chemistry-General
physics-
A block of mass 12 kg is attached to a string wrapped around a wheel of radius 10 cm. The acceleration of the block moving down the inclined plane is
. The tension in the string is (I of wheel
kg
)
![](data:image/png;base64,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)
A block of mass 12 kg is attached to a string wrapped around a wheel of radius 10 cm. The acceleration of the block moving down the inclined plane is
. The tension in the string is (I of wheel
kg
)
![](data:image/png;base64,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)
physics-General
physics-
' O ' is the center of a square ABCD.
and
are four forces acting along the sides AB, BC, CD and AD as shown in figure. What should be the magnitude of
so that, the total torque about 'O' is zero ?
![](data:image/png;base64,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)
' O ' is the center of a square ABCD.
and
are four forces acting along the sides AB, BC, CD and AD as shown in figure. What should be the magnitude of
so that, the total torque about 'O' is zero ?
![](data:image/png;base64,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)
physics-General
physics-
A cylinder of mass M and radius R starts falling under gravity at t=0 as shown in figure. If the mass of chord is negligible, the tension in each string is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALoAAABkCAMAAAAG5NqcAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAALoUExURf////v7+/Dw8PPz88fHxxMTE0ZGRsHBwQAAADExMbW1tVtbW6KiosPDwzc3N4ODg2RkZIyMjG9vb9HR0Ts7O5aWlnd3d+Xl5ePj4/z8/Pr6+rGxsZGRkZ6enqurqyUlJaampn9/f6GhoV5eXktLS6qqql1dXRAQEA8PD0pKSuHh4U1NTQgICLOzs+7u7kBAQERERE9PTxcXF1NTU1JSUj8/PwMDA0lJSVBQUFVVVRgYGCAgIDQ0NAYGBlRUVCcnJ1hYWCgoKDU1NUFBQQ0NDaenpxYWFtTU1G5uboCAgL29vRERETY2NmhoaISEhMTExBQUFPn5+UVFRQsLC+Dg4Nzc3AkJCdjY2IaGhq6urlZWVsjIyAUFBUJCQoqKioKCgpubm1xcXP7+/tDQ0MnJyfj4+MDAwB8fH9XV1d/f3ywsLAICAqioqN7e3jk5Ofb29r6+vvT09BkZGejo6BISEiEhIefn57S0tImJiWZmZv39/e3t7SoqKgoKCvX19ZmZmaWlpcbGxmFhYTo6OrCwsIGBgXl5ecvLyy4uLu/v72tra46Ojn5+fnZ2di8vLx4eHuvr6/f39zw8POTk5J+fn5ycnN3d3VdXVzMzMz4+PgQEBLa2tgEBAUdHR/Ly8srKymVlZYiIiKmpqVpaWg4ODunp6WNjY8LCwqysrG1tbdPT0zIyMsXFxRoaGtvb2wcHB2JiYnV1dRsbG87OznFxcbe3t7KystfX1ysrK0hISL+/v8/Pz4+Pj52dnWBgYNLS0pCQkJiYmFFRUeLi4ry8vHt7e6Ojo6CgoPHx8WxsbK+vrykpKRwcHC0tLYWFhaSkpOrq6hUVFY2NjYeHh5OTk7q6uuzs7CYmJtbW1iMjI3R0dCQkJGlpaUxMTNnZ2bi4uJKSkrm5uZWVla2trXx8fHJyck5OTmpqah0dHV9fXyIiIpeXl+bm5gwMDM3NzWdnZ9ra2nh4eD09PTAwMLu7u8zMzH19fQAAAMVvId8AAAD4dFJOU/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////8AKM62NwAAAAlwSFlzAAAXEQAAFxEByibzPwAABD1JREFUeF7tm0Fu6yAQhrOcE/gG3iK2nIETeeVbIG99PdZmX5xg808awriRHq0eX6SUpBiGf4YBU/f236LSz79HsEsq/Tk2+sT0zYyp1IDwkekrmVRqwGeqrzSkUgM+VX1KpQZ01VvQVW9BV70FXfUWdNVb0FVvQVe9BV31FnTVW9BVb0FXvQVd9RZ01VvQVW9BV70FXfUWdNVb0FVvQVe9BV31FnTVW/CHVXcfmT6/MV25VLjCuM6jlIF8fEsfLmNIp9I3DFkdkkFSnKZfw7UHfdRCWhtL3mjRyyxE+DleeRTxV4agRU9LKqUf315ExpjR2ktBM9Ea3zf5I12PCw6C9bk7TXMq7Q2eD7gpTxWT1seFI+n7Rxkh1V6ZQW+Y2TNQwdocoDq3sVEW0HnaUrHAOfcNXQh3czTrregxQGc91lvAKkjaMQpxRKcvCqxHkIcLz4a5M1CSz2popuAAyS6QT6U9qHJjWKdAlm2RCbgzn304K4kzLgtaq2BQuG7Fcs2akN0lFHDH0NmuzsUyZ3zdwdAcYY1fYFp6mAwF5pwUYRQ1IA+cAfeGHF87DhOCzuZi/6Ng6Qf9okGpUCNAw5sgx/DhDeACjCR0BjqghM9hd9PSYB8htJxgdrM0pDDZgLm4zZGkDIV1Bml6RN0EvnIsEvMU55GErpEkanQ9xv17JmxZw7r4mpHFFF68QfcQukoSuixSN2mKYZGFs+U1zElqsakUWfNv0FwcUREmdJCu6sx05oKXGJxzLERh2A7MlWQtXkmaHdUCczs2UTNdg87MzwqSBE4BNtYS4LHn6fSGi6az6iOIpWApRhHZWEs8mV5PSTvK4yyqmv5cPfeoQCtIb6JZymeQVPWrAfNUPfeIHcKUQWeUYbH+s4CpTtPySLFDUN1Zifcx8nimfIfGO6qpOqfYrJuLAXN+L1OdrRZi05kt9e0Di0rcRCjYiIH/HZscJX62mrIdg2f3P69g+rCohFSCuuGqVeRnexjMwayF1zBrWfrAuQntiPL6DX0j3jmiryTrGHMM9oJ+hkqi1ZQN0FfvqRKoEHqgBAv2CT5sMG6Y7rJJB2n2wl0S3NVJnMvui1g3sJOHGyMlOqGEhi7cm+YBy1Y+uI1j5mJoxA3N+X19SxeBC0Q3yA/yXYxofxoVBaX5JM8jH/IwMJDKnBdcOYeJ6SvJyPQsg+cwzsLqyu7wcliJTqbOC3D6VDlk3ITjDXisgif9jjBMTne8O1HPpAsu/t3hcfRWP9E8QHOVh43EkLOJyke27AiviLM2WsEOMAXE+uN+xi7cOuwhkyOc/WVpyR2DD2X/FhytmAYrTy8PRkveEi16EaE9UaqqFx2vS2gd2znKy/E9q1Jmv5jIS9YvRogd/QqEIYuoLcTX/U3y4kW9nsUwTffi/mHUc/p2G2MgP74uvyLhQnL5Z4SLIdzpdDqdTqfzzO32BbVdxRbbG8DVAAAAAElFTkSuQmCC)
A cylinder of mass M and radius R starts falling under gravity at t=0 as shown in figure. If the mass of chord is negligible, the tension in each string is
![](data:image/png;base64,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)
physics-General
physics-
A block of mass 2 kg hangs from the rim of a wheel of radius 0.5 m. On releasing from rest, the block falls through 5 m height in 2 s. The M.I. of the wheel will be
![](data:image/png;base64,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)
A block of mass 2 kg hangs from the rim of a wheel of radius 0.5 m. On releasing from rest, the block falls through 5 m height in 2 s. The M.I. of the wheel will be
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAABwCAYAAADG4PRLAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAAg5SURBVHhe7Z1/TE9rHMeNzQx/mF/lZ4X1w6+YGpW6GtPNKCyZH7s2171TM2tNflxc43YZkyXNRJoflyGXcHE1FpafW6Qf95Ysu7goqRBK32/v6/P0uPciSt9z6jynz2s7q+dz+na28/qe5zzneT7PeVqhGXnw4AGOHTuGNWvWYOrUqfDw8ICDgwPs7OzQu3dvuLu7IzAwEIsXL8b+/fuRn58vP8m8o8kFVlZW4tChQ5g0aRL69OmDkSNHIiQkBGvXrhXxCxcu4Pr160hPT8fRo0cRGxuLOXPmwM/PD/3794ePjw/i4uJQXFws/2PLpskEVldXY9OmTXBxcYGbmxsiIyORmZmJV69eyb/4PDU1Nbhz5w7Wr1+PYcOGiSt04cKFLV5kkwjMyMiAt7c3HB0dsX37djx9+lTuaRxv3rzBiRMnxNVIV/HBgwflnpaH7gKjo6PFPS08PNxmcR9itVrFFdmtWzdRzTb0ajYTugoMCwtD165dcfr0aRnRh7y8PHh6esLLywvl5eUy2jLQTeDcuXPRs2dP5Obmyoi+kDhfX1+MGDGiRd0XdRFI1WXfvn1x+/ZtGWkaKioq4O/vj1GjRuHly5cyam40F0gNig4dOiArK0tGmhaSSC3diIgIGTE3mgq8d++eaFDEx8fLSPNAz5Ht27fHqVOnZMS8aCpw8uTJmDBhgiw1L9S7Qw/+Zm/UaCbw2rVr6NSpEwoKCmSkeaFHDKpKN2/eLCPmRDOBs2bNEl1iRoK64QYPHgyLxSIj5kMTgYWFhbC3t8f58+dlxBg8efJEtIYPHz4sI+ZDE4ExMTGi6W5E5s+fb7iaQUs0EThx4kRERUXJkrFISUkRjRnqPzUjNguk5y4atztw4ICMGAtqVJHAGzduyIi5sFlgTk4OXF1dxU9bKSoqws2bN2VJG6qqqsSY4+7du2XEXNgs8OLFi+IbXlpaKiONg8b6Bg0ahI4dO2L16tUyqg1jxozBunXrZMlc2Czw5MmTYpzPVo4fP45WrVqJjTqktYTu0ZSWYUZsFkgn3snJSZYaz/Pnz8XwEw0LaT38RD1EixYtkiVzYbPA1NRUIZByXYzK+PHjsWLFClkyFzYLpI5jZ2dn0ZFtVEaPHi0SocyIzQLv378vGh+UTWZESkpKRBIU3avNiM0CCeqFoYwzI0Kd7JT4RF80M6KJQGp8zJw5U5aMRVJSElq3bo2dO3fKiLnQRCANnFKnMVVXRiMoKEg8mmzcuFFGzIUmAqm3g7rTNmzYICPGgLrP2rRpIwTS0JIZ0UQgsWXLFpFxTRnYRoFGIvr168cCG0JZWRl69eqFHTt2yEjzkp2dLRovJI4EGrWRZSuaCSSowdC5c2fcvXtXRpoHqgVophNlplFeKgv8AmiaGHUeNyfLly8XVSel2t+6dYsFfgk0JEQZ2UuXLpWRpuXIkSNo167dv+kd9BzIAr+QK1euiKp02bJlMtI00PzCtm3bYuvWrTJS29XHAhvB5cuXhcSmypCmAVu68mj62v9hgTZA8wJpImZAQIBu+aLU+l2wYAG6dOmCPXv2yOh/sEAbefjwIWbPni3ui9QbQg/9WkFTsKmxQikTJKouWKBG0KSXAQMGYOjQoaLHprHDT3TF7d27VwwRde/eXaRffC7jjAVqCJ18SnWn6daURzNjxgwkJiaKh26avfthLw7Ni6eResqXoeRcqiop05qSqJYsWdKgt1awQJ04e/Ys5s2bJ+a5031yyJAhYm4f5a9MmTIFwcHBGDdunMiPoR6V4cOHixEPet3Il0ylZoE6Q9UfvS/mzJkzogVJc+pXrlwpqkaapkb3OWoANXbCJgtUHBaoOCxQcVig4rBAxWGBisMCFYcFKg4LVBwWqDgsUHFYoOKwQMVhgYrDAhWHBSoOC1QcFqg4LFBxWKDisEDFYYGKwwIVhwUqDgtUHBaoOCxQcVig4rBAxWGBisMCFYcFKg4LVBwWqDgsUHFYoOKwQMVhgYrDAhWHBSoOC1QcFqg4LFBxWKDisEDFYYGKwwIVhwUqDgtUHHotMwnctm2bjJgL5QTSYsvJycni7b4JCQn1brT8OAmkdQTr2l/XRotFPnr0SB7R2CgnMCoqSgihd2jTkuX1bV5eXmLdCl9f3zr317XRos60oCV9UYyOcgLpZegk0GKxyIj2ZGZmimPExMTIiHFRTmBoaKg4uc+ePZMR7aG1n+gYtKil0VFWYHl5uYx8TPWrZ3j46Amqql7jz8wbKPi7TMRfFN1Fxs1sPP/0OiECWveJBepEfQKtFcXYsigErh4BiE/ch/DpAXAc6I3Nuw4hbk0Exno6w/+bVSj5zApALFBH6hNYU12JCwmR6NZnKH7PK0d1dRm+83GCR+iPKK14jdL0HbDv7YbU/E+vQ8ECdaQhVegfv/4MV89A3HlNJStWTPHGtOX7xD4UnICzizuO3yqtLdcBC9SRhgjMSY5+W4V+jbwXVHqDHyZ7IWSZXJouLwUursPxW/anP88CdaQhAjP2LoXdAC/UOqpExNiBCFhYuzCkJfsg7O2ckJxRIsp1wQJ1pF6BLx8j6acw+PkHYn9aFgpz0/F98FgEfbsKOYV/Ie2X9fjKzx/Ru86gwio/8wEsUEfqFVhjhbWm9lfr24d92t5hsVpRLXfWWC2Qf/YRLFBHGlKF2goL1BEW+D7KCnzxQjQxdeHq1assUC+mTZum+xV46dIlcYy4uDgZMS7KCZw+fbo4uQ4ODmIFaz22Hj16iGPExsbKoxoX5QTSgshUxZ07d063LS0tTRzj8ePH8qjGRTmBzPuwQMVhgYrDApUG+AejzqjP6Rx4DgAAAABJRU5ErkJggg==)
physics-General
physics-
A rod is free to rotate about 'O' as shown. It begins to rotate. When it has turned through an angle '
' its angular velocity 'w' is given as
![](data:image/png;base64,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)
A rod is free to rotate about 'O' as shown. It begins to rotate. When it has turned through an angle '
' its angular velocity 'w' is given as
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHcAAACVCAYAAABitWUDAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAAy3SURBVHhe7Z0LVFVVGsdvAiriAx9j0vi2NVqoSCrpQggVUcwHjhNqxijKqDmhzJSPFGYmzHGa5WvKRxbmykhoaFIKxXyMAuEYPkpNUVMhUAFTFMV8of/h23dfCwWVe++5d9/D91vrLL3f2Vw55+fZd9/9+LYBjG5huTqG5eoYlqtjWK6OYbk6huXqGJarY1iujnE4uXfu3EFmZiYWL16MJUuWiGPp0qWYO3cuVq1ahWvXrsmSjDJyb9++jS1btghJr732Gvbu3SvPVOTChQto3749DAZDpcfWrVtlyYoUFxdjw4YN2L17N27evCmj+sbuci9fvoyFCxeiR48eFSRFRETIEhUhMfPnz0e/fv3Qt2/fu0dAQABCQkKQk5MjS1YkJiZGvG+dOnXQrVs3REdHixqAagK9Yne5mzdvviu0du3a6NChAyZMmIBvvvlGlrAOn3/+OZ588sm7/5bp+PLLL2UJ/WF3uQUFBZgxY4aojqnKvHHjhjxjfUpLS7Fx40bMmzcPQUFB8PHxwZ49e+RZ/aG5XKpG161bh4SEBNy6dUtG7Q/9XiS7Kk6ePIlDhw7JV46JZnJLSkqwc+dOBAYG3q0Cv//+e3lWbc6dO4fmzZvDzc0N48aNQ0ZGBsrKyuRZx0ETufRUUKOFPkNJKv05ffp0/PTTT7KE2ly8eFFU26b/lE5OThgwYECVLXhV0Uyuh4eHuDE9e/ZEenq6POM4XL16FYmJiaIlbpL80ksvybOOgWZy27RpI24INZQcndWrV2PgwIFISUmREcdAc7mzZ8+WUceGrsnR0FzurFmzZJSxNSzXQlJTUxEVFSW+o6sGy7WQ0NBQcZ3u7u6Ii4uTUTVguRZC3aReXl7iWuvVqyc6a1SB5VqBEydOwN/fX1yvi4sL0tLS5Bn7wnKtxPnz5zFo0CA0aNAAycnJMmpfWK4VuXTpEg4cOKBMVyXL1TEsV8ewXB3DcjWG5nytX78eZ86ckRHbwXI1hmZn0n3o37+/zYc8Wa7G7NixA3Xr1hX3gibl2RKWawMWLFgg7oWzs7OYqGcrWK4NoEl/Q4YMEfeDpuTaajoty7URubm5YpDh/ffflxHtYbl2YN++ffJv2sJybQytZ6L+5zlz5oj7pCUs14ZQy5nE0n2ZMmWK5n3QLNdG0Jxt0z2hxtWVK1fkGe1guTbg9OnTYoov3Y/OnTsjPz9fntEWlmsDaFlK06ZN0bBhQ5uuTWK5NmL//v3Ytm2bfGUbWK6OYbk6huVqAK0zUgGWa2UOHz4MPz8/sb6I7oM9YblWhPJ7PPfcc+K6e/fubffMOizXikydOlVcM60+UGF5Ccu1EitXrhTXS8dHH30ko/aF5VqB7777TqRAout99dVXZdT+sFwrQJPRIyMjMXToUKVSQ7BcK6Jazg+Wq2NYro5huWaQlJSEH3/8Ub5SF5ZbTVasWCGui7LbPCgDnQqw3GpAQ3aurq7iuiZNmqR80jSW+4gcPXoUrVu3Ftc0fPhwh0jazXIfAcoF6e3tLa6H0h7aY1GXObDcR6CwsFDkfmzRooVD5X9kuY8IJfs8ePCgfOUYsFwdo6bcshJkbd+A1XEfIDXzIHi/EfNQTm7+nk8x0s8LvYNCMG5cGPy7tcczwROw88QFWUJ7aNEW7Zbi6Cgl92zWx/Bq5IweY+bjtJyQX3x8GwZ2cEa93wQjPUf7uUmUEY5+d0f4Hvsw1JFbehxh3dxhaOKLXfc8pMc2zEO98vd6KnQ+Lmq4TUJRURG6d+8ufm/6ykOJwxwZZeR+HRcpynuPfxv3VYiXD+G3nahnqDne3vGDDFoXWiA9YsQI8Tu0atVKDMA7OmrIvVmA6YGtRPkJ72TI4C+5in+GGTeV6hWxHNbenIZ6m2iwnd6fknNSml09oITc0mOp6NmE5h81QOwX2TJakeRYY+pbt6dGYP9lGbQStLdRp06dxPsvW7ZMRh0fJeRmb/4HmpaXNRja4N3dla+A2xM3Hc5UpoEnkvZZ2W45lLORFkbrCSXkZrw7CY+RONcu+M+RSzJakbzkN0SjymBogbhNx2SUeRBKyN04b6Qoa3D3RnzGcZwrKsTZs2fvHoVF57A3/nU0FHIbIS7Jsfb3sRdKyE2a87xRbp0meDYgCMOGPo/g4OC7x5Bhw9G3Z0e4CLn1EZeg3n4CKqKE3PV/GWaU29gba7YfwA+5OSL7uOnI/SEPO1ZEwlXItfzJpY2VKT+FnrdXJZSQu33JOKPcel5Yf7TyxlL2ulmoQ2Ue88DqVPP3BDStDKC9+k6dOiWj+kQJuYeSY9FIiKu6tbzzXxHGRpd7V3x20LxuSNpZ2zRNhtb1qLLUUiuUkHsleyO6u1OV64qYz47IaEUSXjdW3U2eGYtsM7p8qcfJ9DvRyoCasLe9EnJRVoCoAcb5SaMWbJbBX1KC2Be6iPODZiXe3z35ECgtkGnbdJouQ50WNQE15JazP36maA23Gzgb933TvbAPA9s6w1DfExsOl8jgo0NPKW0YSb1Qet7p+l6UkYvrZ/Bn0b/8OFbuOieDRjLfnSzeK/TNZFiSc43mQtUk1JFbTmnODozwbgpXDx+sSv6f2Fp8y4exaNvQDf0nLcIFx9sI064oJZe4fvYA3ooaC99ne6FfYBCCgkcgNm4TtE+mpz+Uk2uitLgI+flncNmM8T1KWWCrFHwqo6xcc6FMbZSTwtPTEzk5OTJaM9GVXPqK06WL8SsTfeWhQYeajG7kXr9+HcOGGTs66N/Ozq580L8moQu5NA3VlCaIMqNu3bpVnqnZ6EIuPbWjR4+Gk5OTWD/LGNFcLuXytwXUxUgDA3qYTG4tNJf7yiuvIC8vT7Ri6XOwJnTYq4Lmct3c3NCsWTMx1Eafh+3atcOYMWPE5oWOPqNfdTSXS0etWrXEfnb0pylGB+3znpFR2TzlB0NVsN5nUVgDzeXSLH6qko8fPy5GZGhHLNoZyzRoTluxrFmzRv7kwyGxgYGBogFVU4buzEVzuTExMTJaka+++gp9+vQRZVxcXJCYmCjPPJjJk40jRPQz3377rYwylaG53Ad9FaKNg00bGNKcpmPHHjwfedGiRaIsVe9r166VUaYq7CqXoJV1Tz/9tCg7fvz4Kj9L6cmmp5XKVVUbMBWxu1zik08+EWXp8/fIkSMy+jP0foMHDxZlqKVNr5mHo4RcaiR17dpVlF++fLmM/gw9zTR/mZ7Ymj4YUB2UkEtMnDhRlA8PD5cRxlKUkWva+jsgIEBGGEtRRq6pJUy7ezDWQRm506ZNE+VffPFFMWSXlpYmzzDmooxc6rWi8iNHjhQ7VlL6gqysLHmWMQdl5FKKoLCwMDRu3Fj8HFXPPMnNMpSRS/3Evr6+4me8vLxYrBVQQi6llO/Vq5coTzmNaT88xnKUkEvp5MeOHQsPDw+kp6fLKGMpylTLNA+KspEz1kMZuYz1Ybk6xi5yacIcDwBoj83lFhcXw8fHBx07dnS4tPKOhk3lUqMpJCRExGmxVmZmpjzDaIHmcmfOnCliNFmcElRTrH79+khJSRFxRjs0l0srDsrKyjBjxgzxmuY/VWe2I2M+msuNjo4Wcv38/MRrGrdlbIPNPnOprzg+Pp4nk9sQmzaoGNuiiVyqhtu2bcty7YwmcktKStCyZUuWa2c0kZt78oQQSwct4WTsg8Vyz5/YizXLFuGvMdGYM/evWPlxCo6eLcHiJYvxp2nTdLPThyNivtw7V/Dvt/6Izh274HcRkZj3ZiwiRgWisasLmnv2w4fpubIgYy/MlHsLn70RCidDbUxbvUvGjGQlxOBXVCW7/RpvfcEzKuyJWXKLstaipbMBTXwjcf/2iTfwzmR/8Xnr2mEwdhfyuh57UX25d65i+RTjutrguUkyWJGitOV4og41qJwwdWX1V84z1qHacm9fPIzQzrWF3LBFlSW+LufSbgxqW1eU6T1xMfSdbF5dqi33as42+DYzfs0ZtaCKkZ2yXPzBp7ko0/mFv1VSdTO2oNpyr+elo6+HUa7v1PcqT0l/uwCR/h6ijP/L74Bz1tiH6n/mXsvHy/7Gp7Jp93Ccqmw/29snEe7dqLxMLUR98LUMMram+nJxB1uWGtfSGlwex8IteTL+Cwr/ix4Ny8+36IddBZYkrmcswQy55Q/mpaOI8H1CCH7CNxyH7/lQ3fT30eXnXDD1PZ5gbk/MkksUH9uOUT7GkZ/Wz47Eio8/ReqmZCyZ+Xu0cH8cYbEJKJVlGftgtlziRnEu4pfG4Pk+3njKsxv8+wfhhfAofJqeXV55M/bGIrn3wpMs1MKqchm1YLk6huXqGJarY1iujmG5Oobl6hiWq2NYro5huTqG5eoYlqtjWK5uAf4PpnlX9hcxof0AAAAASUVORK5CYII=)
physics-General