Maths-
General
Easy
Question
Let
then
- f(x) is continuous but not defferentiable at x = 0
- f(x) is both continuous and differentiable at x = 0
- f(x) is neither continuous nor differentiable at x = 0
- f(x) is a periodic function
The correct answer is: f(x) is neither continuous nor differentiable at x = 0
![table row cell t subscript t plus 1 end subscript equals fraction numerator x over denominator open parentheses r x plus 1 close parentheses open curly brackets open parentheses r plus 1 close parentheses x plus 1 close curly brackets end fraction equals fraction numerator open parentheses r plus 1 close parentheses x plus 1 minus open parentheses r x plus 1 close parentheses over denominator open parentheses r x plus 1 close parentheses open square brackets open parentheses r plus 1 close parentheses x plus 1 close square brackets end fraction equals fraction numerator 1 over denominator open parentheses r x plus 1 close parentheses end fraction minus fraction numerator 1 over denominator open parentheses r plus 1 close parentheses x plus 1 end fraction end cell row cell therefore S subscript n end subscript equals stretchy sum from r minus 0 to n minus 1 of t subscript r plus 1 end subscript equals open curly brackets table row cell 1 minus fraction numerator 1 over denominator n x plus 1 end fraction comma end cell cell x not equal to 0 end cell row cell 0 comma end cell cell x equals 0 end cell end table close end cell end table](data:image/png;base64,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)
![f open parentheses x close parentheses equals Lt subscript n rightwards arrow infinity end subscript invisible function application S subscript n end subscript equals open curly brackets table row cell 1 comma x not equal to 0 end cell row cell 0 comma x equals 0 end cell end table therefore text Lt end text f open parentheses x close parentheses equals 1 text and end text f open parentheses 0 close parentheses equals 0 close](data:image/png;base64,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)
Hence f(x) is neither continuous nor differentiable at x = 0
Clearly f(x) is not a periodic function
Related Questions to study
maths-
If m is the slope of tangent to the curve
then
If m is the slope of tangent to the curve
then
maths-General
maths-
If
is equal to e7, then ![stack l i m with x greater-than or slanted equal to 0 below fraction numerator f open parentheses x close parentheses over denominator x to the power of 3 end exponent end fraction equals horizontal ellipsis horizontal ellipsis](data:image/png;base64,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)
If
is equal to e7, then ![stack l i m with x greater-than or slanted equal to 0 below fraction numerator f open parentheses x close parentheses over denominator x to the power of 3 end exponent end fraction equals horizontal ellipsis horizontal ellipsis](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGwAAAArCAYAAACdO20ZAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAAA4pJREFUeNrtW0FoFDEUDaUssoiwSClFSkGkiIdS8CAi4qWIyFJkL9KDh1IQKaV4E08eRCg9FCneehARWSgiUooIIksp0ssiIiKlIOJBRIQ99FCKFOr/9A/GmEySmYzuzPwHj+78ZDLT//cnPz9/hcgnpoFznvfM0X2MDNED7FdkI8CNhOO9ofsZGeASsEP8AOyVlD6acMzTwHVWbXigcb5KhjlFf0fJYGmwToZjBEQD2NTI54EzKceeTbD+MSy4A7ylkb8EntfIpwxGuEttMs4CX7OKw+EZcF/ihNS2DawY7nurBCiTwAeafhUahxEQm8BBjXzPEqQs0Ocxixf9ZBWHDeV3DG17lntfAS8A3wGPssH+Dc4AW4a2uCkRcZOMEbfX4ikxMHDNehjjQecMbSh/StPiRMz4HHQExiLwuqHNFNYfB64Aq8DDwHbMlDhD4zACRomXDW26jXMf8IVioDrwcdk2zjsUANhkoYGpqEMx7RvSGlUhAx/T9GtS5CijsKmpE8D3DrLQQG/5ZunDyV8Nrgh9aihL3Kf9l0va6IbwTy/Nx6yNuYcuNaTKout+ChS+k3dE60+NIrYOhdG3Lc/E6arBS3gyLJOXxcmWyWhtCqMxwz4E/AwcAK4Br5Icsxa74u+zrW7HvgO7AluahVyVbdF+pqb0w2ORJYN8gH0hPHSpIVUWXVcN/aoOY/p+k7NkrqFLDakyU/rIV85TYkapIVVmSh/5yhkZpYZQNmXpk0TOyCg1pMpM6SNfeVGhTpehr62pIVVmSh/5yrNUFh6z4LnYxaIbrEg4CfzCk2a+tigdVkM+gMctWIQzyarIz6J/jVWRHxwB3uPtRP6wW3YFNEV8CZkKPK7fJNZTPNenujcCVgm3y24wPGLBX5O4nF1hhdIaGRjZIllSuFT3RusXehaWdg8V1RBY6zAihcNx/ywq/4mDtz0XB4Wd8jd+JcU7+lT3Fh518bssYMHRg2zeti3+LNrpEemLOF2re0sBVAJWzy553DMM/BETXqtIWybtUt1bGixScFDxWM+wkmrc0cN6U3qYa3VvKTBGU+JHcVBuZssi4BqGxZo1jzUMP68mfD+f6t7CY5CiOVTENIXKrl4VGc8UJbbIqH30jCTHLL7VvYVGhSLEYen6ExlPB9mrbFNipFgs2MEk7GzC9/Op7mUYpkRU1iPLlMjoAjQomqyzKvIB9qr/iF9clhWKir+YNAAAAV10RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXVuZGVyPjxtcm93PjxtaT5sPC9taT48bWk+aTwvbWk+PG1pPm08L21pPjwvbXJvdz48bXJvdz48bWk+eDwvbWk+PG1vPiYjeDJBN0U7PC9tbz48bW4+MDwvbW4+PC9tcm93PjwvbXVuZGVyPjxtbz4mI3gyMDBBOzwvbW8+PG1mcmFjPjxtcm93PjxtaT5mPC9taT48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bWk+eDwvbWk+PC9tZmVuY2VkPjwvbXJvdz48bXN1cD48bWk+eDwvbWk+PG1uPjM8L21uPjwvbXN1cD48L21mcmFjPjxtbz49PC9tbz48bW8+JiN4MjAyNjs8L21vPjxtbz4mI3gyMDI2OzwvbW8+PC9tYXRoPoSKqLAAAAAASUVORK5CYII=)
maths-General
maths-
Set of all values of x such that
is non-zero and finite number when n N
is
Set of all values of x such that
is non-zero and finite number when n N
is
maths-General
maths-
The period of the function
is
The period of the function
is
maths-General
maths-
Let
is a prime number and [x] = the greatest integer
The number of points at which f(x) is not differentiable is _______
Let
is a prime number and [x] = the greatest integer
The number of points at which f(x) is not differentiable is _______
maths-General
maths-
If the line
is one of the angle bisectors of the lines
and
then the value of k is
If the line
is one of the angle bisectors of the lines
and
then the value of k is
maths-General
physics-
A particle when projected in vertical plane moves along smooth surface with initial velocity 20m/s at an angle of 60°, so that its normal reaction on the surface remains zero throughout the motion. Then the slope of the tangent to the surface at height 5 m from the point of projection will be
![](data:image/png;base64,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)
A particle when projected in vertical plane moves along smooth surface with initial velocity 20m/s at an angle of 60°, so that its normal reaction on the surface remains zero throughout the motion. Then the slope of the tangent to the surface at height 5 m from the point of projection will be
![](data:image/png;base64,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)
physics-General
physics-
Consider a particle moving without friction on a rippled surface, as shown. Gravity acts down in the negative h direction. The elevation h(x) of the surface is given by h(x) = d cos(kx). If the particle starts at x = 0 with a speed v in the x direction, for what values of v will the particle stay on the surface at all times?
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)
Consider a particle moving without friction on a rippled surface, as shown. Gravity acts down in the negative h direction. The elevation h(x) of the surface is given by h(x) = d cos(kx). If the particle starts at x = 0 with a speed v in the x direction, for what values of v will the particle stay on the surface at all times?
![](data:image/png;base64,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)
physics-General
physics-
System shown in figure is released from rest. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring ![open k equals 40 N divided by m blank a n d blank g equals 10 m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
System shown in figure is released from rest. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring ![open k equals 40 N divided by m blank a n d blank g equals 10 m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
A smooth track in the form of a quarter circle of radius 6 m lies in the vertical plane. A particle moves from
under the action of forces
is always toward
and is always 20 N in magnitude. Force
always acts horizontally and is always 30 N in magnitude. Force
always acts tangentially to the track and is of magnitude 15 N. Select the correct alternative(s)
![](data:image/png;base64,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)
A smooth track in the form of a quarter circle of radius 6 m lies in the vertical plane. A particle moves from
under the action of forces
is always toward
and is always 20 N in magnitude. Force
always acts horizontally and is always 30 N in magnitude. Force
always acts tangentially to the track and is of magnitude 15 N. Select the correct alternative(s)
![](data:image/png;base64,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)
physics-General
physics-
Ball I is thrown towards a tower at an angle of 60° with the horizontal with unknown speed (u). At the same moment ball II is released from the top of tower as shown. Balls collide after two seconds and at the moment of collision, velocity of ball I is horizontal. Find
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zTp08L1V0kEuHNmzfC/FbX2pRYnp6e9X4KNisrS5gTyeVy9OjRQ+Oriu7cuQOZTNboNqdMmYK//vpL40bVpUuXYsWKFYiPj4dKpcL58+c1JuLe3t44evQojhw5goyMDCQmJna4u3saSiy5XI7Q0FDh5t6lS5dqVG5danZivVuZgNpVbKVSicuXLwtteXl5GDRoEM6ePQulUgljY2NhYq1QKJCRkSH83FlDPDw8YGpqimvXrgltIpEIXl5emD17NsaNGwcTE5N6r7OxscH8+fMxZ84cSKXS5h6WQWlomIuPj0d6ejpKSkqwadMmHUTVsGYlVmZmJmJiYuDo6Ijk5GSkpaUBqJ1PeXl5Yd68eaiqqsL9+/ehUCgQEBCAhQsXIjIyEmKxGPHx8WCMISgoCBYWFvj6668bD0gsxpAhQ/D3339r5wg7iIYm53VvsKSkJGEJp6E3nU60dYW1vLycubm5MU9PTzZ58mTm4eHBNm3axEaOHMkYY8zPz48NGzaM+fj4MAcHB5aVlfXebUZERLDg4OC2htahuLu7s4MHD2q0KRQK5ujoyAAwAMzMzIw9ePBARxFqavNJMwsLC6SlpcHKygqpqalQqVRYtmwZxo0bh5iYGEgkEhQWFuL58+e4cOECPD0937tNV1dX3L17t62hdSgNzbHMzMywZ88e4fH69ev152rct7PMzs5OyH76p1//+vfvz/bt29dgdZg1axbz8fFhKpWqPYpRs4gY++9tcOvWLVRXVzecge1IrVYb5BUIPFVXV8PGxgYODg71+l6+fImysjI4OTnpILKGaSQWIdrC9dLk8vJypKSkCHMDJyenZs2xOqu6a8jqDB8+vMFr3wwCrzH2+PHjzMbGRpgjhISEMIVCwWt3HUJ5eTkLDAwU/ma2traNXoOl77Q+FJaWlmLOnDk4duwYgNrTPoGBgfD29tbmbjosxhjS09Nx5MgRvHnzBkDt2YjffvsNvXr10nF0zaf1oTA1NRUXL14UHkskEty+fRu5ubna3lWHVVVVBYlEIiRWUlISrly5gkmTJuk4shbgUQZLSkpYQECAUNJ79uzJEhISeOyqwzlz5gyzsrIS/nYBAQGsuLhY12G1GNdPhSdOnMDRo0fBGINYLEZERASGDx/Oa3cGLzk5GVu3bhUeT5kyBZMnT9ZhRK3XKZcbioqKhJV9c3NzfPLJJygoKEBeXh5MTU0p+bWgU65C2tra4v79+/jss89QUFAAAOjWrRsWL15ssDda6JtOWbHq+Pn5oaKiAufPn8cvv/yCwMBA9OvXT9dhdQidsmLV2b17N/755x+MHz8eH3/8MSWVFnXqxLK3t8eSJUuQlJREv9mjZZ06sUpLS/Hs2TPMmjUL33zzTb3LrEnrddo5Vk1NDebOnYvo6GhUVVXBw8MD/fv3x8WLF/XuVipD1CkrVmVlJSIiIiCTySCVStGtWzcsWLAAly5dwsaNG+mHobSgU1assrIy4aZaT09PGBkZITMzU+jv3bs3LTu0UadMLMJfpxwKCX+UWIQLSizCBSUW4YISi3BBiUW4oMQiXFBiES4osQgXlFiEC0oswgUlFuGCEotwQYlFuKDEIlxQYhEuKLEIF5RYhAtKLMIFJRbhghKLcEGJRbigxCJcUGIRLiixCBf/B51uvm+hhiNvAAAAAElFTkSuQmCC)
Ball I is thrown towards a tower at an angle of 60° with the horizontal with unknown speed (u). At the same moment ball II is released from the top of tower as shown. Balls collide after two seconds and at the moment of collision, velocity of ball I is horizontal. Find
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJYAAACvCAYAAAAfdCeHAAATRElEQVR4nO3deUxU1xcH8O8MMI4FFCwoMIKAytbgglQbtf5woUFiG6tosAQqmkpFtC41qbVqXUDrQmPqvgRLcN+qIqRGNAoipYoUFxQQFHQEFLGODgjM3N8fhFdHFlnmMjNwPomJc+/Me+eRM+feue+9GRFjjIEQLRPrOgDSMVFiES4osQgXlFiEC0oswgUlFuGCEotwQYlFuKDEIlxQYhEuKLEIF5RYhAtKLMKFsa4D6IxevHiBlJQU3Lt3D0ZGRhg0aBCGDRuGrl276jo0raHEakdKpRLTp09HSkoKxGIxPvjgAzDGoFQqwRjD9OnTsWbNGojFhj+QiOh6rPbx5MkTjB07Fi9evAAAPHjwABKJBACQn5+PkSNHAgDc3NyQmJiILl266CxWbTD8t0Y7u3v3Lm7fvi38KywsRGlpqUbb7du3UV1dLbzm1atXGDVqFHr06IHr169DLBbjxIkTQv+GDRtgYWGBS5cu4dGjR/D19dXFoWkXIy0il8vZpEmTGAAWGRnJFAoFUyqV7I8//mAAmIeHByssLGQqlUp4TXBwMHNzc2PV1dWMMcbGjh3L/ve//zHGGKupqWFOTk5syZIlwvbt7e3Zhg0b2v/gtIgSqxV27NjBALCcnByNdolEwiIiIjTaXr9+zWQyGTt48KDQFh0dzezt7ZlarWb5+fnMwcGBXb16VehftmwZc3V15XsQnNFQ2AoikQgAYGRkVK/93bbbt2+DMQZ/f3+hbfDgwQCAkpIS5ObmQq1Ww8XFReifOHEiFAoFlEolr0PgjhKLs4KCAojFYpibmwttvXv3hkgkglwuR0FBAUQiEXr06CH029raQiQS4dmzZ7oIWSsosTgzNjYGYwxqtVpoU6lUAGornomJCdRqNdhbH85ramoAwKCXHQw3cgPh7u4OACgqKhLacnNzoVKp4OjoCFdXV4jFYsjlcqE/OzsbjDHY2NgAAB49eoTZs2c3uZ+cnBwO0bceJRZnLi4ukEql2LZtm9CWlpYGqVSK7t27w9XVFYwx3Lp1S+jfuXMn+vTpA2Pj2vXrsrIy7Nixo9F9HDt2DKNHjxbWyPQBJRZnRkZGCA8Px6FDh1BaWgoASExMxJAhQwAAVlZWsLCwQFxcHAAgNTUVaWlpWL9+vbCNug8LrIG17LKyMkREREAul2PhwoW8D6fZKLHawYIFC+Do6Ijhw4fjzJkzKC4uxtKlS4X+WbNmITk5GQcOHMDUqVPxxRdfCCvxQNOJ9d1336GkpAQAEBMTgz///JPz0TQPJVYrKBSKem2VlZUaq+1vE4lEuHDhAjw9PREWFgbGGMrLy5GdnY3s7Gw4ODigqqoK33//PUJCQrB9+/YGt/NuYuXl5WH//v0AIJwCWr58eVsOTWvoJHQLnTt3DufOnYOzszNOnDgBf39/mJmZYe/evXB0dERRURESExMxZswYjfN9xsbGOHnyJA4fPoyoqCh89dVXQqKIRCLY29tj69at8Pb2rrfPuor1roqKCgCAt7c3CgoKIJFIhDad09XKbGdXUVHBcnNz2YMHD4RTPY25desWA1DveVlZWczGxoYdPHiQ2djYsLi4ODZgwACeYTcbVSwdkUql6NevX7Oe29gcSywWIzY2FjU1NRCJRAgKChLmW7pGcywD0FhieXh4wNfXV6N9wYIF7RpbYyixDEBjifX23Kvu/43Nx9obJZYBaGq5oal2XaLE6iD0pVLVocQyAM2pWJRYpMVoKCRcvC+x3n6OvqDEMgBUsQgXVLGITtDknbQKDYWECxoKCRdUsQgXVLEIF7TyTrigoZDoDFUs0mJUsQgXNHknXNDknXBBQyHhgoZCwsX7koYqFmkTqlhEq2iORbigORbhgpYbCBc0FBIumlONqGKRVqOKRbSKJu+EC5q8Ey5o8k64oKGQcEHnCgkXVLEIVzR5J1rVmsk7YwyZmZlc42oKJZYBaOlQ+PjxYwQFBcHLy4t7bI2hxDIALa1YMpkMU6dO5R5XUyixDEBrJu+6/hFNSiwD0Jzlhqaek5qainXr1iE7O1vboTWKEssAtGXlfdWqVThx4gSSk5MxYsQIlJWVcYnxXfRbOgakpetYjDFMnToVbm5uqKqqQu/evZGQkIDg4GCeYQKgimUQWluxRCIR3NzcAAASiQR2dnYoLCzkE+Q7KLEMgDZX3tvr9A8llgGgqxsIF3RpMuGipRf6VVRUID09HYwx3Lp1C4wxFBYWIj8/H0VFRfj333+5x0yfCg1Ic4fCyspKTJs2DdOmTQMAqNVqVFZW4urVqwAApVKJ7t27c42VEsuANHfybmlpCUtLS41+FxcXbnE1hIZCAyESiWjyTrSvqcSq69cnlFgGoqnEoQv9SKvRUEi4oKGQcEMVi2gdVSzCxfvmWJRYpFVo8k64eF9FoopFWsXQKla7nivMycnBqVOnYGVlhdDQUFRXVyM2NhbFxcWYNm0anJ2d2zMcg0KT9ya4uLjg4cOH2LlzJwDAxMQE48aNw08//YS8vLz2DMUg0eS9Ce+edbezs2vvEAySoQ2FNMcyEDQUEi7edxJa3+htYlVVVWH79u0oLy/XdSh6gSrWezg6OiI/Px+VlZUAgEOHDgH4712nUqkQFxcHd3d3hIeH4/nz5+0dol6iOdZ7TJw4EVKpFC4uLvD394dMJoNYLEZKSgpyc3MxePBgBAcHIz8/HwCgUCjaO0S9ZUgVq92vef/www+RnZ2NvLw8uLq6QiKRoKioCHZ2dpgzZw5u3rwJsVgMtVoNAHj58mV7h6iX6FxhM5iammLgwIGQSqUQi8Wws7PDzZs3ERsbi1mzZsHS0hJWVlYAam9lIjQUttrjx4+Rl5eHbt26YdSoUbC3t0e/fv3g4+Oj69D0Ap0rbCU/Pz8oFArs3LkTGzduhLW1NaKjo9GlSxddh6YXqGK1waJFixAeHg5nZ2cEBwdjwoQJug5JbxjacoPe3LCalJSE9PR0xMXFAQCCgoL07o+lSzR5bwWVSoX58+djzZo1MDc3B6B/70B9QENhC+3atQsmJiYIDQ3VdSh6i4bCFnrx4gVWrFiB48eP6/ybfvUZnStsoVWrVsHHxweffvqprkPRa1SxWiAnJwd79+5FVlaWLsMwCDR5b4FFixZh7ty56NOnjy7DMAiGto6ls4p17tw5ZGRkCFc3kKYZ2lCok4qlUqmwYMECREVFwdTUVBchGCSqWO+xY8cOmJqaIiQkpEWve/z4MTZv3ow3b95gxIgRGj9EdOjQIaSmpsLY2Bjjx4+Hr6+v0Hf//n2sWrUKxcXFGDBgANatWwcjIyOtHU97MLSKBdbOnj9/zrp27cqioqKYUqls9usuXrzIbG1tWWxsLFOr1UK7Wq1mW7ZsYWPGjGEKhYJVVlayjz76iGVmZgr9fn5+rLS0lDHGWExMDFu/fr12D6odODg4sNOnTzfYt3r1ajZhwoR2jqhpzapYDx8+hFKpFB5LJBL07du33vOqq6tx6tQpJCcno7y8HF27dsXQoUMREBAgfJnqihUrYG1tjcjISGzbtg2bNm1670+g3b17F5MmTcKxY8cwZswYjb6KigqsXr0av/76K8zMzAAA/v7+CAkJQWZmJu7cuYMBAwbA2toaADB9+nSd/+Raaxja5L1Zcyxzc3PExMTAw8MDUVFR9W7hAmon4/369cO8efNw+fJlPHz4EDdu3MDPP/8Md3d37Nq1C9nZ2fj999+RkpKCkpIShIWFYebMmQgLC0NNTU2D+1apVAgKCkJISAhGjhxZr//atWsoKSnBgAEDhDYfHx9kZWWhqKgIvXv3RkZGhrD9tLQ0g1yI7bBD4ZUrVxgAdvz48Xp9a9asYTKZjNna2rLRo0dr9EVERDBbW1smk8mYnZ0dW758uUZ/dnY269u3L5s8eXKD+z169CgDwOLj49nq1atZeHg4S0xMFPpXrlzJALCSkhKhLT8/nwFgx44dY4wxdvDgQTZ27Fg2depU5ufnx+RyeXMPW284OTmxkydPNti3cuVK9vnnn7dzRE1r9lu37h3x7qR39+7d2LZtG9auXYs9e/YgJycHxcXFAGqHxrNnzyIsLAwLFy5ESUkJ5HK5xuvd3Nxw6dIlnD9/HrGxsfX2e/jwYZibm6OiogIzZsyAmZkZxo8fjwMHDgAAysvLIRKJhCtOgdqhGgCKiooAAIGBgTh79ix27dqFxMRE2NraNvew9QozoIrVpjHh1atXiIyMRFhYGIKDg+Hr6wuxWCxc+nL58mXU1NQgKCgIe/bsweLFi5GQkIAbN25obEcmkyE6OhoLFy7EixcvNPru3LmDvn37IiAgAHZ2dli3bh2GDBmC+fPnQ61WQyqV1hsm6oa9t//YXbp04f6l+Tx1qpX3Q4cOQa1W48cffwRQ+10Mffr0QUpKCgDgypUrMDY2RkJCArp3746oqCg4Oztjw4YN9bYVGhoKmUyGNWvWaLQbGRlpVBiRSITAwEA8ffoUcrkc9vb2UKvVGh8uHj9+DACwt7dvy+HplU51Evry5cuQyWQwNv7vw6WHh4dw69aNGzdgbW2NVatWYfPmzRCJRBg4cCDu3btXb1sikQjLli3Dli1b8OzZM6F96NChePLkicZzLS0tIZFI0KtXLwwbNgxA7VpVnczMTHTp0kVjLcvQGdrkvU2J9fTpU/Ts2VOjzdnZGa9evQIAPHv2DGVlZfD398fQoUMBADY2No3eefPll1/C2tpa4zTPt99+i9zcXI07onNzczFz5kyYmJjAy8sLAwcOxPXr14X+jIwMRERECBcNdgQNJVbd47fb9aV6tSmxpFKpkER1Xr58KVSw6upqPHz4EOvWrRP6X79+3ejHfSMjI8yYMQP79+8X2ry9vfHDDz9g+vTpKCoqwsWLF3H16lWsXbsWQO0ffM+ePdi3bx/kcjmuXr2K+/fvIzIysi2HpncaSqzTp08L1V0kEuHNmzfC/FbX2pRYnp6e9X4KNisrS5gTyeVy9OjRQ+Oriu7cuQOZTNboNqdMmYK//vpL40bVpUuXYsWKFYiPj4dKpcL58+c1JuLe3t44evQojhw5goyMDCQmJna4u3saSiy5XI7Q0FDh5t6lS5dqVG5danZivVuZgNpVbKVSicuXLwtteXl5GDRoEM6ePQulUgljY2NhYq1QKJCRkSH83FlDPDw8YGpqimvXrgltIpEIXl5emD17NsaNGwcTE5N6r7OxscH8+fMxZ84cSKXS5h6WQWlomIuPj0d6ejpKSkqwadMmHUTVsGYlVmZmJmJiYuDo6Ijk5GSkpaUBqJ1PeXl5Yd68eaiqqsL9+/ehUCgQEBCAhQsXIjIyEmKxGPHx8WCMISgoCBYWFvj6668bD0gsxpAhQ/D3339r5wg7iIYm53VvsKSkJGEJp6E3nU60dYW1vLycubm5MU9PTzZ58mTm4eHBNm3axEaOHMkYY8zPz48NGzaM+fj4MAcHB5aVlfXebUZERLDg4OC2htahuLu7s4MHD2q0KRQK5ujoyAAwAMzMzIw9ePBARxFqavNJMwsLC6SlpcHKygqpqalQqVRYtmwZxo0bh5iYGEgkEhQWFuL58+e4cOECPD0937tNV1dX3L17t62hdSgNzbHMzMywZ88e4fH69ev152rct7PMzs5OyH76p1//+vfvz/bt29dgdZg1axbz8fFhKpWqPYpRs4gY++9tcOvWLVRXVzecge1IrVYb5BUIPFVXV8PGxgYODg71+l6+fImysjI4OTnpILKGaSQWIdrC9dLk8vJypKSkCHMDJyenZs2xOqu6a8jqDB8+vMFr3wwCrzH2+PHjzMbGRpgjhISEMIVCwWt3HUJ5eTkLDAwU/ma2traNXoOl77Q+FJaWlmLOnDk4duwYgNrTPoGBgfD29tbmbjosxhjS09Nx5MgRvHnzBkDt2YjffvsNvXr10nF0zaf1oTA1NRUXL14UHkskEty+fRu5ubna3lWHVVVVBYlEIiRWUlISrly5gkmTJuk4shbgUQZLSkpYQECAUNJ79uzJEhISeOyqwzlz5gyzsrIS/nYBAQGsuLhY12G1GNdPhSdOnMDRo0fBGINYLEZERASGDx/Oa3cGLzk5GVu3bhUeT5kyBZMnT9ZhRK3XKZcbioqKhJV9c3NzfPLJJygoKEBeXh5MTU0p+bWgU65C2tra4v79+/jss89QUFAAAOjWrRsWL15ssDda6JtOWbHq+Pn5oaKiAufPn8cvv/yCwMBA9OvXT9dhdQidsmLV2b17N/755x+MHz8eH3/8MSWVFnXqxLK3t8eSJUuQlJREv9mjZZ06sUpLS/Hs2TPMmjUL33zzTb3LrEnrddo5Vk1NDebOnYvo6GhUVVXBw8MD/fv3x8WLF/XuVipD1CkrVmVlJSIiIiCTySCVStGtWzcsWLAAly5dwsaNG+mHobSgU1assrIy4aZaT09PGBkZITMzU+jv3bs3LTu0UadMLMJfpxwKCX+UWIQLSizCBSUW4YISi3BBiUW4oMQiXFBiES4osQgXlFiEC0oswgUlFuGCEotwQYlFuKDEIlxQYhEuKLEIF5RYhAtKLMIFJRbhghKLcEGJRbigxCJcUGIRLiixCBf/B51uvm+hhiNvAAAAAElFTkSuQmCC)
physics-General
physics-
A ball of mass ‘m’ is rotating in a circle of radius ‘r’ with speed v inside a smooth cone as shown in figure. Let N be the normal reaction on the ball by the cone, then choose the wrong option.
![](data:image/png;base64,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)
A ball of mass ‘m’ is rotating in a circle of radius ‘r’ with speed v inside a smooth cone as shown in figure. Let N be the normal reaction on the ball by the cone, then choose the wrong option.
![](data:image/png;base64,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)
physics-General
physics-
System shown in the figure is released from rest when spring is unstretched. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring k = 40 N/m and ![open g equals 10 m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
System shown in the figure is released from rest when spring is unstretched. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring k = 40 N/m and ![open g equals 10 m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
Two blocks of masses
are connected by a non - deformed light spring. They are lying on a rough horizontal surface. The coefficient of friction between the blocks and the surface is 0.4. What minimum constant force F has to be applied in horizontal direction to the block of mass m1 in order to shift the other block? ![open parentheses g equals 10 m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGYAAAATCAYAAABiMHgQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAtNJREFUeNrtWE1kHVEUHlFPRYSIireoElFvERUqoiqixBMVT4WIqK5KRUVFNlFRWYXIoioiREQWXZSKripKRVU8ESoiiy66iS4qojxVEfEMyTl8ieu+c2fu3HmTyWI+Pt47c+/Muefc83Ov52W4KpyBVWKZ2JGZ5HqhgfiSuBtlEk+Yy2wXiC7s+Lg4VX7PwfYi7hG3M7uHYoX4NOY7+ojfNVkZPqhBGbshbdwlviHuBYxpJi4Rd8BlyJLGLeIB0pEr8rB1uya/T9xKKjzrgffEFyiUJmwSS8r/QciSxjQ2TZxN9xnOkbAFB11injh+DbsYCcPEBUH+jjiacNE+QNS4RspGSGS/0mv8F2KvYXAjHPcXBWuduEicSskx/P2iIH+EZypmoGcbnHlEPCQ+xvMW4ltihfif+DpAH3b6qkVE/Sb60F+1ETulEDL/gR75rFROGHgDRWoKv5mT+PCTkH49iHEcUzHomoPhVXyEc37AsKz/Hez8PNY2AvltbLw22zQjOGXFoJtnaYccfHEJ3/AyzqezgvxXQJ5MOmL8gDlVQc9NRIaKPzCiJM87tsj8vL8O667aLJbDvlXItccp1hjf8mzAep4gFXsR5K4t8jAOjaV6OkZKZWL7RughfrO4ekgqlR0Z0sVNLZWZ9Iwqj9Ii52Ezfk+Tg1NqUtlX4kNt0BBaV6kIrqUYMVzgBwR5USv+Jj2jyqO2yLxB9onPHNZcU/yldplD8oPhnPE8RccMIbXoWNPa5QWch3REkbu2yKuOtwPj8EVgcWtGauhSxqyjQPal6BgPqWIC3VQOu1q/4viktMWucpsWWUc38adQm20gdn7bwl1NCX15FS1nEeeZhoQdElaTWmCwUxTsZSGnV5BWvBjysBb5Av+gp49NU3BYt6mmW11idhrSW4b4MF5iMsaUKwH2+pLS13djciGzYd0xb6h7IppQEI+RLjYQMRmuAOdQXcnAFedchQAAAMJ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bWk+ZzwvbWk+PG1vPj08L21vPjxtbj4xMDwvbW4+PG1pPm08L21pPjxtbz4vPC9tbz48bXN1cD48bWk+czwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21yb3c+PC9tZmVuY2VkPjwvbWF0aD4MHyohAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Two blocks of masses
are connected by a non - deformed light spring. They are lying on a rough horizontal surface. The coefficient of friction between the blocks and the surface is 0.4. What minimum constant force F has to be applied in horizontal direction to the block of mass m1 in order to shift the other block? ![open parentheses g equals 10 m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGYAAAATCAYAAABiMHgQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAtNJREFUeNrtWE1kHVEUHlFPRYSIireoElFvERUqoiqixBMVT4WIqK5KRUVFNlFRWYXIoioiREQWXZSKripKRVU8ESoiiy66iS4qojxVEfEMyTl8ieu+c2fu3HmTyWI+Pt47c+/Muefc83Ov52W4KpyBVWKZ2JGZ5HqhgfiSuBtlEk+Yy2wXiC7s+Lg4VX7PwfYi7hG3M7uHYoX4NOY7+ojfNVkZPqhBGbshbdwlviHuBYxpJi4Rd8BlyJLGLeIB0pEr8rB1uya/T9xKKjzrgffEFyiUJmwSS8r/QciSxjQ2TZxN9xnOkbAFB11injh+DbsYCcPEBUH+jjiacNE+QNS4RspGSGS/0mv8F2KvYXAjHPcXBWuduEicSskx/P2iIH+EZypmoGcbnHlEPCQ+xvMW4ltihfif+DpAH3b6qkVE/Sb60F+1ETulEDL/gR75rFROGHgDRWoKv5mT+PCTkH49iHEcUzHomoPhVXyEc37AsKz/Hez8PNY2AvltbLw22zQjOGXFoJtnaYccfHEJ3/AyzqezgvxXQJ5MOmL8gDlVQc9NRIaKPzCiJM87tsj8vL8O667aLJbDvlXItccp1hjf8mzAep4gFXsR5K4t8jAOjaV6OkZKZWL7RughfrO4ekgqlR0Z0sVNLZWZ9Iwqj9Ii52Ezfk+Tg1NqUtlX4kNt0BBaV6kIrqUYMVzgBwR5USv+Jj2jyqO2yLxB9onPHNZcU/yldplD8oPhnPE8RccMIbXoWNPa5QWch3REkbu2yKuOtwPj8EVgcWtGauhSxqyjQPal6BgPqWIC3VQOu1q/4viktMWucpsWWUc38adQm20gdn7bwl1NCX15FS1nEeeZhoQdElaTWmCwUxTsZSGnV5BWvBjysBb5Av+gp49NU3BYt6mmW11idhrSW4b4MF5iMsaUKwH2+pLS13djciGzYd0xb6h7IppQEI+RLjYQMRmuAOdQXcnAFedchQAAAMJ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bWk+ZzwvbWk+PG1vPj08L21vPjxtbj4xMDwvbW4+PG1pPm08L21pPjxtbz4vPC9tbz48bXN1cD48bWk+czwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21yb3c+PC9tZmVuY2VkPjwvbWF0aD4MHyohAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
physics-General
physics-
In the figure shown the spring constant is K. The mass of the upper disc is m and that of the lower disc is 3m. The upper block is depressed down from its equilibrium position by a distance
=5mg/K and released at t=0. Find the velocity of ‘m’ when normal reaction on 3m is mg
![](data:image/png;base64,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)
In the figure shown the spring constant is K. The mass of the upper disc is m and that of the lower disc is 3m. The upper block is depressed down from its equilibrium position by a distance
=5mg/K and released at t=0. Find the velocity of ‘m’ when normal reaction on 3m is mg
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAACZCAYAAAA2LPStAAAQz0lEQVR4nO2de1BU5RvHv7AsuuDK7iKgiSigLpggoXgB+hmgKAqKTalhF8eatJmGyTRT6o8yLzONWcqoTU6WpqPWRJo2kiCaFxRJDZCLqQgs1+SywC6wLLvP7w+GHdeza6i7nBc6nxln4Dkv7zyP3/O+zznveS8OREQQYApHvh0Q4CKIwiCCKAwiiMIggigMIojCIIIoDCKIwiCCKAwiiMIggigM4sS3A1qtFh0dHXarXy6Xw9Gxn917xDMrV64kAHb5FxwcTHfu3OE7xMeG95ZSU1ODnTt34s0337R53QqFAkaj0eb12hveRSEiODs7w8XFxeZ1Ozg42LzOvqBfdLYajQYA0NbWBr1eDwDQ6XTQarV8umU3mBfl66+/hq+vL7Zv346EhARERETg8uXLePfddzF69GhcunSJbxdtDvOiJCYmoqWlBYmJicjIyIDBYEBhYSH27t2LDz/8EIcPH+bbRZvDvCguLi5wdnaGn58fHB0d4eXlhREjRgAAvLy80NzczLOHtod5Uf6LMC+KwWAw+72rq8vizwMJ5kXJzc3Fa6+9hosXL0KlUiE4OBgqlQotLS1oaGiAj48PVCoV327aFAcifqcYLViwAPPnz8fKlSttXrdEIkF+fj7GjRtn87rtCfMt5b8IE2/0586dQ2Njo83rHjZsmM3r7At4FyU2NhbXr19HYWHhv5a9ffs2Ojo6EBQU1Ku6ly9fjqFDhz6ti30O7znlcdi0aRPu3LmD77//nm9X7Eq/yikikYjziDwQ6VeiODk5CaKwhtBSGEQkEg3Yt/gH6VeiaLVaqNVqVFZWoh89nzw+PH6K7hU5OTk0d+5cksvlBICkUimJRCKSSCQUGRlJp0+f5ttFm8O0KLt27SIA5OvrS2fOnKHU1FSKi4ujjo4OKiwspH379pFYLKby8nK+XbUpvL88WqOyshIff/wxPvroI2zatAkA0NDQgGeeeQaDBg3ChAkT4OzsjDFjxqCpqQk+Pj48e2xD+L4rrJGYmEgrVqwws12/fp1cXV1p7dq1NHv2bJLJZLRmzRqePLQfTL7Rt7e3Y8iQISgqKoJSqTS7durUKdy9exdisRjR0dH9bgS4NzDZfanVaoSEhGDUqFGca3FxcTx41LcwKcqIESNQU1ODI0eOYMWKFdBqtfjuu++Qk5MDFxcXlJWVQalUYsGCBZg1axbf7tocJkUBgG+//RZLlixBbm4uDh06BD8/PyxatAiBgYHQaDTIysrCiy++iKioKBw/fpxvd20L30ntUURHRxMAmj59Omk0Gs71hoYGmj17NpWUlPDgnf1gtqVkZ2fj6tWr+N///ocrV65g4cKFmD17NgICAqDVapGVlYUTJ07Az89vwCV7Jp++ACAkJARJSUlYt24d6urq8M033yA/Px9SqRR3796FUqnEwoULMX/+fL5dtTlMitLU1AR3d3fU1tbC09OTb3f6HGa7r4dnzBMRqqqq8M8//wAA/P394ebmxodr9ofXjPYIwsLC6P333yetVkvr1q2jkSNHkoODAyUkJJCnpyeJRCKKjo6m7Oxsvl21OcyK8vfff5OLiwuJxWKSyWR09OhR6ujoMF2/efMmpaSkkFwuJ7VazaOntofZ7ymenp5wdXWFXq+HQqGAQqHAoEGDTNcVCgW8vb0hlUpN61cGDHzfFdZYtWoVxcXF0ZkzZygqKorEYjG5ublRUlISTZw4kUQiEQUFBVFaWhrfrtocJp++9Ho9XF1dcfnyZUyePBlA9yquW7duob6+HgaDAUqlEr6+vjx7ah+YfPqqq6tDYGAgAgMDTTYXFxc899xzpokTIpGIL/fsDpM5ZeTIkaipqUFaWhoA4Pfff0d8fDw8PDwQExMDsViMcePGYe3ataiurubZWzvAd/9pjV9++YWGDh1KPj4+JBaLaf369XTlyhWqq6ujqqoq+uGHHyguLo7GjBlDOp2Ob3dtCpM5BeheEDR69GjU1NRgyZIl2LVrFxQKhVmZyspKJCcnY9u2bfDz8zPZ6+vrUVVVZfrdyckJzz77LKqrq3H//n2TPSAgwOyJjhWYzCkA8MUXX0AulyMmJgbHjx9HcHAwZs6cicmTJ6OhoQFnz57F1atXsXz5cjNBAMDNzQ15eXmYNWsW4uPjceDAAQDdj9FJSUloaGjA/v37IRaL+QjtX2FSFCLCli1b8NNPPyE2NhadnZ04deoU8vPz0dzcjMbGRixZsgQHDx7kCAIAYrHYlHumTp0KuVwOACgpKYGLiwuOHz/O9hANz92nRVQqFUVGRpq9wT8JYrGYtm7dSkREt2/fptdff/2p6+wLmGwpXl5euHLlCvLy8jB16lQAQEFBAXJyctDW1obW1lYolUrExsb2av1JUVERUlNTsWfPHiZzCAe+7wprfPDBBzRp0iTat28fKZVKkkgkFB0dTSkpKfTGG2+Qj48PSSQS+vzzz63WIRaLaenSpTRq1ChSqVR96P3Twawoer2efHx8CABFRERQTU2N2XWj0Ujnz5+nsLAwqq6utliHWCymZcuWkbu7OwUGBnLqYBUmXx4B4Nq1a7h//z4kEglu3LiBH3/8ERUVFTAajTAYDPjjjz9w9OhRFBUVYfDgwVbrmThxIjIyMlBTU4OoqCjU1tb2YRRPCN93hTVCQ0Npy5YtpNPpaNu2bRQYGEiOjo4UHR1NTk5OJJVKaenSpVRQUGC1jgcTfU5ODkmlUgoICGC+xTApSn19PQGg2tpaM7tOp6OKigqqqKggvV7/yDqMRiM5OTmZRCEiunjxIslkMuaFYbL7cnZ2BgDOfl5qtRrNzc1obm6GTqez+vcdHR349ddf0dXVhfLyctTV1QEApkyZgjlz5qCkpARhYWE4ePAg2tra7BfIE8LsMEtcXByGDx+OL7/8Ep999hnS0tJQVlaGefPmITs7G1qtFjExMdi4cSPCwsLM/rapqcn0LR/oHlEeO3YsNBqN2fAL0L3W3t3dvU9i6jV8N1VrVFZWklQqJUdHR5LL5XTgwAFqbW01Xb9+/TqtXbuWFAoFNTc38+ip7WGy+wK6uzBnZ2c4ODhAJBJh1KhRGDJkiOm6t7c3AgICIJPJBt6eX3zfFdZYtmwZLV68mMrKyigpKYmcnJxIoVDQq6++SqGhoSQWiykgIICOHDnCt6s2h8mcotPp4Orqihs3bpi2/NBoNCguLkZ9fT30ej2USiVn7cpAgcmxr4aGBoSFhZnNER4yZAgnoQ9UmGwpRAR3d3fs378fCQkJAIDS0lLk5uZCo9Ggra0NSqUSM2fO7B8DjI8Lr53nI9ixYweNHTuW0tPTacaMGeTs7ExTpkyh1atX06JFi8jDw4Pc3Nxo9+7dfLtqc5gVxWAwUFhYGAGg8ePHU2lpqdn1zs5OOnnyJAUEBPSrEeDewOwj8b1791BcXAyJRIKqqipkZWVBrVbDYDCgpaUFv/32Gw4fPozKysp+uafXI+H7rrBGbGwsJScnU1tbG23fvp28vb0JgGl114gRI2jVqlVUVlbGt6s2h8lEr9VqTYuDHpwF2dTUBK1WCzc3N0ilUh49tC9MPhJrtVpERkZi+PDhZna5XG6aBDGQYTKneHh4oKioCOnp6Wb21tZWREdHY86cORg7dixeeukl3Lhxgycv7Qjf/ac1du/eTb6+vtTY2GiyHTt2jCZMmEB5eXmUnp5O7733Hsnlcqqrq+PRU9vDrChGo5GmTZtGMpmM0tPTiYho7969FBcXZyrT3t5OM2bMoNzcXL7ctAtMJvoe1Go1IiIiUFRUhLlz50IsFqO8vByvvPIKCgoKkJGRgfDwcPz8888DahY+kzmlB5lMhsLCQhQXFyMyMhJ1dXVobGxEXl4e/Pz8kJaWhmPHjg0oQQBGx76skZqairNnz5qWSAxUmG4pD9PV1TXgWoUl+pUoBoNBEIU1/iui2CWnTJo0Cbdu3epX5yz6+vpizZo1djkE9HGxyzBLQUEBsrOz+9W+KsnJyVCr1Xy7AcBOohARRo8ebTpl7nG5d+8etm7dCmdnZ3zyySd9cg6KPU5kfVKYyynNzc3IyMjA6tWr0dLSghUrVvDtUp/DnChisRhvv/02AgMDsWPHDrNrnZ2daGtrg9FoNM31IiLU19fz4ardYE6Unm6EiJCWloadO3cCAG7evIlx48Zh06ZNWL58Ofz9/ZGVlYUNGzYgPDwcKSkpfLptW+wxoAbA6kKe3tDW1kY7duwgiURC69atM9nDw8MpNTWViIg2b95M8fHx1NXVRaWlpeTl5fVUPr/88su0bdu2p6rDVjDXUoDuowCTk5Px559/Ys+ePSgtLQXQ3Yp65oJ5eXlh2LBhEIlE8PT0HFBTV5kUpYcJEyZg+vTpkMlkfLvSpzAnSmVlJQoLC0FEyM3NxZQpU0w7TTx4ylDPufQP/zwQYO4bfW1tLXbt2gV/f38EBQVh8+bNAIDy8nKEhoairKwMLS0tpm1CKisr8ddff+Gtt97ChQsX8Pzzz/McwdNjl2EWBwcHVFdXP/HLIx8sXrwY06ZNw5o1a/h2xX4t5ejRo/0qFzy4kQ7fcFqKRqPBO++8A4lEYlawq6sLRMTZZKa9vZ1TNisrC1qtFo6O5inLaDRybNbsj1O2J4SHB0CtlSUijl2v1yMoKAj+/v5mf9/V1WVag/momIkICQkJWLBgAcfnx4XTUoxGI0pLSxEdHW1mv3btGnx9fc22dyIinDlzhnMyQ0hICKRSKby9vc3smZmZnLIqlco0i/7fyup0Oly9epWTNy5duoTQ0FCz/yij0Yhz5871Oo7MzEyEh4eblS0uLoZUKoWXl1ev4igpKbGJKJyXx8zMTMrIyOC80Kxfv55jy8/Pp0OHDnHsGzZsIIPBYGarrq6mnTt3cspu3LiR2tvbzWxarZY2btzIKXv48GHKy8vrlW+PE0deXp7FOFJSUshoNJrZamtr6auvvuKU/fTTTzlxPCmc/uHSpUt44YUXzGwtLS0WV9Cmp6cjPj7ezKbX6zF48GBO93Dy5EksWrSIU0dXVxdnx4jTp09j3rx5nLLFxcUIDg42s6lUKovbS1mL4+GN3KzF0ePXw13iiRMnLMbRE7ctsPie4uRk3qudOnXKYrNsb2/nzHi/cOECp8sAgJqaGk53VlhYiEmTJnHK5ufnm3ZZ7aGzsxOurq6csidPnkRiYqKlMJ46jqioKE7ZqqoqzqFs1uJ4UsxEuXbtmmkrpwe5c+cOxo8fb2ZTqVQYM2YMp2xubi6nb25tbbV4h2ZmZnKOczIYDBZXZ2VlZSE2NpZjb2xshIeHh5nNWhw9p0k8HIelrXRzc3MRERHBicPSXOaMjAyLLftJMRPl/PnziImJMStg7Q5NT083LX3rgYggEok4XZelskB3k3/4KebChQucbgfovhtDQkLMbI2NjRa/blqLw9KHLGu+iUQiTtdlqZsDuh9AbPqR7MEEY+kQS61WS/X19Ry7pbKdnZ0WR4crKiosJjRL9scp29TURC0tLb3yTaPR0P3793tVVq/XW9y7xdohn7Y+/LNfTcb7r8DcgKSAIAqTCKIwiCAKgwiiMIggCoMIojCIIAqDCKIwiCAKgwiiMIggCoMIojCIIAqDCKIwiCAKgwiiMIggCoMIojCIIAqDCKIwiCAKgwiiMIggCoMIojCIIAqDCKIwiCAKgwiiMIggCoMIojCIIAqDCKIwiCAKgwiiMIggCoMIojCIIAqDCKIwiCAKgwiiMIggCoMIojCIIAqD/B/enHoSbQD6NQAAAABJRU5ErkJggg==)
physics-General