Maths-
General
Easy
Question
The minimum area of triangle formed by tangent to the ellipse
and coordinate axes‐
- ab
The correct answer is: ab
Given, that a triangle is formed by tangent to the ellipse
and coordinate axes, we need to find the minimum area of the triangle formed.
![E q u a t i o n space o f space tan g e n t space a t left parenthesis left parenthesis a cos left parenthesis empty set right parenthesis comma b sin left parenthesis empty set right parenthesis right parenthesis space t o space t h e space e l l i p s e space i s space x over a cos left parenthesis empty set right parenthesis plus y over b sin left parenthesis empty set right parenthesis equals 1
C o o r d i n a t e s space o f space P space a n d space Q space a r e space
open parentheses fraction numerator a over denominator cos left parenthesis empty set right parenthesis end fraction comma 0 close parentheses space a n d open parentheses 0 comma fraction numerator b over denominator sin left parenthesis empty set right parenthesis end fraction close parentheses space r e s p e c t i v e l y.
N o w comma space a r e a space o f space t r i a n g l e space O P Q space equals 1 half open vertical bar fraction numerator a over denominator cos left parenthesis empty set end fraction cross times fraction numerator b over denominator sin left parenthesis empty set right parenthesis end fraction close vertical bar equals space fraction numerator a b over denominator open vertical bar sin left parenthesis 2 empty set right parenthesis close vertical bar end fraction
T h e r e f o r e space comma M i n i m u m space a r e a equals space a b](data:image/png;base64,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)
Therefore, the minimum area is ab.
Related Questions to study
Maths-
An ellipse has OB as semi minor axis,
and
its focii and the angle FBF’ is a right angle Then the eccentricity of the ellipse is‐
Therefore, the eccentricity of the ellipse is
An ellipse has OB as semi minor axis,
and
its focii and the angle FBF’ is a right angle Then the eccentricity of the ellipse is‐
Maths-General
Therefore, the eccentricity of the ellipse is
Maths-
The number of values of
such that the straight line y=4x+c touches the curve
is‐
Therefore, there are two values of c.
The number of values of
such that the straight line y=4x+c touches the curve
is‐
Maths-General
Therefore, there are two values of c.
Maths-
Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at
Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at
Maths-General
maths-
An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐
An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐
maths-General
maths-
Normals
are drawn to parabola
from the pointA (h, 0) If triangle
(
being the origin) is equilateral, then possible value of h’ is
Normals
are drawn to parabola
from the pointA (h, 0) If triangle
(
being the origin) is equilateral, then possible value of h’ is
maths-General
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,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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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)
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,iVBORw0KGgoAAAANSUhEUgAAAFEAAAATCAYAAADoH+FRAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAk9JREFUeNpjYCAe/IfiX0B8FIhVGAY34EFyMzmYpoAJiLOA+NwgD8QIIN4/yN3I8GOQu287EKcMZgfaA/HBQew+ESB+D6UHJZCElolKdLDLh8zyKQOI1+Mp1+leBiIDNSDeAg1IelQM18j0IKgsDMERiAOeArcBMR+d7JsJxMlkeFwBiF8DMQe9A3EuEIdjES8A4lYoGxSAGnQKQGsg3kumxyuAeDaeZhqpABSRHVjEm6FycBAPxF1oiriA+BYQC+MpTwi1Kckpg9iA+BIQy5Pp8fNA7EHFQGSANufEkfiJQDwFXZEXEK9CE6sH4toBKDZAsZ5DhMd5sIjpAPFzIGbBE4igzsInaM4qwmEOOgBFSh+U7YKUS1AAKLVdQeKLAvFdHOUKLYEetObHl3pAPaX5UHEbNLl2IO4nwh5QIBtDE8kNIoup3dCm3QWk3IkBviGx+6DlIbmA3Ox8Ekt3El1tDTQQQe3AU2hy94HYhES3uhHZ5i2ApmI9fIoOQ9t+StBUyDQAWZmUgAd1Pf8hlVUWQHwbT1ampPcFqujWQBNXJD6FC4HYD4iXAnHsIGrc46sMQLlnGZQ9GYgbyDBfB5pocAFQotoErWhB5ecZfNm5ANrUuTTIekj4AnEOEH+Hpr7XRJRt64DYEprLmKAVBigAg3CoF4VWQMJovajFuCwIgDrYbwgFogAQ/wXitUB8nAizQqHNtj9A/A7aIjHF09QCBbo0FrnluJpRfkQ6ZLCBw9CALhgMjtkGTepDDZhCA1FmoB2iAx1YGKogZCAtBwBz1KeefDDEBAAAAJd0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1cD48bWk+eTwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+PTwvbW8+PG1uPjQ8L21uPjxtc3FydD48bW4+NTwvbW4+PC9tc3FydD48bWk+eDwvbWk+PC9tYXRoPvUy+oMAAAAASUVORK5CYII=)
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
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARgAAAEFCAYAAAA4xvjJAAAgAElEQVR4nO3dXWxbZ/0H8G/4I2Y0oBYgarGNHm3tegZDOQWJnqQTORGgON2g7i42hxs7XCSuBIo9UTmVkDwLJHfsws4FcpIL3OzG3SRkV2K1qwFxhdY4AuRTNGZviRQXIdmVhuJdsHMQL8//IrXJu19yjs859u8jVVsSx37q2l8/53n7DTDGGAghRAcfM7oBhJDeRQFDCNENBQwhRDcUMIQQ3VDAEEJ0QwFDCNENBQwhRDcUMIQQ3VDAEEJ0QwFDCNENBQwhRDcUMIQQ3VDAEEJ0QwFDCNENBQwhRDcUMIQQ3VDAEEJ0QwFDCNENBQwhRDcUMIQQ3VDAEEJ0QwFDCNENBQwhRDcUMIQQ3VDAEEJ0QwFDCNENBQwhRDcUMIQQ3VDAkJZlpgcwMJ0xuhnEQihgSGvW5/CzRQCLP8PcutGNIVZBAUNasv7mG8DwMIA7eONNShjSGgoY0oIMXvU/jZ8s/QRTAO688SYoYkgrKGBIU+tzP8M7scsYPzkO1xSAO368SkMxpAUUMKSJdbz5BvDCsycBAOOuKQDAYpoShjRHAUMOl3kV/qd/gpmTD74ed2EKABbToIghzVDAkENl0ouYco1v+844LseGASyCOjGkmQHGGDO6EcSk1udw7pQfdw76+XAMa2/P4ORBPyd9j3ow5ECZV/14+iYDY7v/rCE2DODOG6AZa3IYChhygAzSi1PYcXXUcBLPvkBrYkhzFDBkH+uYmz6PxSkX9s0XACeffQHDAO74T2E6QyFD9kdjMGSP6YEBLDa+msJNtrAzaDLTGDi/uPOXpm6CLRwUR6RfUcAQQnRDl0iEEN1QwBBCdEMBQwjRDQUMaVm5XDa6CcRiKGBIS2KxGM6cOYNqtWp0U4iF0CwSaapWq2FoaAgvvvgi7t+/j3g8bnSTiEVQwJCmAoEATpw4Ab/fjzNnziCRSEAQBKObRSyALpHIoWRZRj6fh8/nAwDE43FcunTJ4FYRq6CAIYcKh8MIBoOw2WwAAFEU4XA4kE6nDW4ZsQIKGHKgeoi4XK4d34/H4wgEAlBV1YhmEQuhMRiyL1VVMTQ0hGQyCZ7n9/z85Zdf3vFfQvZDAUP2FYvFcO/ePUSj0X1/rqoqnnrqKaysrMDhcHS5dcQqKGDIHtVqFaOjo1hZWYHdbj/wdtevX8eNGzeQTCa72DpiJTQGQ/YIh8OYmZk5NFwAwO12o1wuI5/Pd6llxGqoB0N2kGUZk5OTKBQKutye9BfqwZAdAoHAgeMu+xEEAYIg4Nq1azq2ilgV9WBIQzqdxtLSElKpVFu/V61WMTQ0hGKx2FgvQwhAAUMeOOqsULNZJ9KfKGAIAODq1av48MMPEYlEOvp9VVVx5swZZDIZcBynceuIVVHAEM0ucTq9xCK9iwZ5CQKBACKRyJHHT1wuF1RVRTab1ahlxOqoB9PntJ5mpmlrsh31YPrc5OQkEomEZvcnCAIkSUIsFtPsPol1UcD0sWvXrjXWsWgpGAxiaWmJjtckdInUr/TerEjT1gSgHkzfCofDmJ6e1m0ntM/nQz6fhyzLutw/sQbqwfShcrmM8fFxFAoFXVfeZrNZzM3NIZPJ6PYYxNyoB9OHtJqWbsbpdMJms9Hxmn2MAqbP5HI51Gq1Pcdg6iUSiSAcDtPxmn2KAqbPtLtb+qh4nockSZifn+/aYxLzoDGYPmLUzA4dr9m/KGD6RL064/LysiFv8vn5edy9e5eqQvYZCpg+sb06o1GoKmT/oTGYPrC7OqNRqCpk/6GA6QO7qzMahapC9h8KmB53UHVGo1BVyP5CYzA9rFl1RqNQVcj+QQHTw8y64ZCmrfsHBUyParU6o1GoKmR/oDGYHtVqdUajUFXI/kA9mB5klWMrrdJO0jnqwfSgbu836hRVhex91IPpMVYrHUJVIXsbBUwPsersjFlnu8jRUcD0kKNWZzQKVYXsXRQwPUKrS41arQZZllEqlRpVAf75z382ZnscDgdOnz7duH19+f9RNzBa7dKOtIYCpkdMTEzgwoULcLvdbf2eLMvIZrO4ffs2crkcbDYbBEEAz/M4fvw4AMBms0EURQBbQVYqlRq/v7q6imq1ClmWG4dLjY2NQZKktqfIx8fHMTMzA6fT2dbvEfOigOkB7U735vN5LC0t4fr16+A4Dk6nEyMjI5Ak6Ui9n1KphFwuh1u3biGXy0EQBHg8HrhcrpbChqatew8FTA9o5ZwVVVUxPz+PhYUF2O12eDweuN1uXRfi5XI5LC0tIZvNwul0YmZmpumllBnOrSEaYsTSEokE83q9TW/DcRzz+/2sWCx2qWX/oygKSyQSTBAE5vV6WaVSOfC2lUqFCYJw6G2IdVDAWJiiKIzjuAPfjKlUivE83/RN3U31sJudnWWbm5v73iYajTK/39/llhE90EpeCzuoOmM+n8fo6GhjViaRSJhmXYzX60WxWMSxY8dw5swZxGKxPWfDUFXIHmJ0wpHObGxsMJ7nmaIoje8pisJ8Ph8TRZEtLy8b2LrWbG5uMr/fz3ieZ4VCYcfPMpkMczqdBrWMaIUCxqJcLhdLpVKNrzc3N5nT6WTxeNzAVnVmY2ODiaK44+/D2N6/I7EeChgLWl5eZpIkNb4uFotMEARL9FoOoigKc7lcLBQKNb5X/3tt76URa6ExGAvavls6m81icnISqVQKkiQZ3LLO2Wy2xireiYkJqKpKVSF7AK2DsZjtGwNjsRhu3bqFZDJp2oOlOnH9+nXMzc0hmUzC4XBYcgMn2UIBYyHbqzOGw2HYbLae3YEsyzICgQASiQSy2SxVhbQoChgLqa9ytdlsffGGK5VKmJycRCaTwejoKFWFtCAag7GIenXGL3/5y7hx40bP9ly243keoVAIExMTVBXSoqgHYxEXL17E+Pg44vE4lpeXe2rMpZn6uFO5XG5sniTWQD0YC0in0/jXv/6FRCLRcwO6rfD7/ahWq3A6nVQV0mKoB2Ny9eqMdrsdwWCwb89KUVUV4+PjeOKJJ/Doo49SVUiLoB6Myc3Pz+Phhx/G2NhY34YLsLVOJplM4o9//CN++ctfNk7bI+ZGPRgTqx+Defz48cZpc/0uFovhd7/7HR5++GGqCmkB1IMxsXA4jC984QuYnZ2lcHnA5/NhbW0N7733HlWFtADqwZiULMtwu9345Cc/SUdI7pJOp/GLX/wCH3zwAT03Jkc9GJMKBAJ46KGHen4xXSdcLhc++OADfOlLX6KqkCZHAWNC6XQaiqLg8ccfb5zmT3aKRCL4xz/+gXA4TNPWJkaXSCZTr8746U9/Gq+99hotjT/ExYsX8dnPfhaf+cxn+mJlsxVRD8ZkYrEYBgcH8ZWvfIXCpYlgMIi//OUvyGazKJfLRjeH7IMCxkSq1SoWFhagKAo8Ho/RzTE9URTx4Ycf4oc//CECgYDRzSH7oIAxkUAggGAwiD//+c99vaiuHR6PB3/729+gqiqy2azRzSG7fNzoBpAt9XrQg4OD8Hq9RjfHMrxeL86cOYNMJoPJyUkKZpOhHoxJTE5OIpFI4PXXX8eLL75odHMsw+FwgOd51Go1SJKEWCxmdJPINhQwJnDt2jUIggCO41Aul2lwt00jIyPI5XIIBoNYWlqifUomQgFjMFVVEQ6HEYlEkMvlLH1wt1EkScLt27fhcDjg8XjwyiuvGN0k8gAFjMG2V2e8ffs2RkZGjG6S5YiiCFmWoaoqVYU0GQoYA5XLZaTTafj9fgBbJV9p5W77bDYbeJ6HLMuw2WwIhUK4cuWK0c0ioIAxVCAQQCQSaeyULpVK4Hne4FZZU338CgCcTidsNhvS6bTBrSIUMAbJ5XKo1WqN82Wr1SpsNlvfHYeplcHBQdy9e7fxdSQSoX1KJkABY5Dt1RmBrcsljuMMbJG18TyPUqm042uqCmk8ChgDxGIxSJK0YzqaLo+Oxm63o1ar7fheJBLB3NwcTVsbiAKmy2q1GhYWFhAMBo1uSk9xOBx7gsRmsyEYDCIcDhvUKkIB02Xbp6W3U1WVjsU8ApvNtu94C01bG4sCpovq1Rl9Pt+en1WrVRw/ftyAVvU+qgppHAqYLgqHwwgGg9RT6TJRFOFwOGja2gAUMF1Sf3EfVPbUbrfjww8/7GaT+ko8HqeqkAaggOmC7fuNDrLfLAhpXbMxrPo+patXr3axVYQCpgvm5+chSRJNQ+uoWq3uGTjfbXZ2lnZbdxkFjM7qx2CGQqFDb7ffNCtpXa1Wa7oK2mazIRKJ0PGaXUQBo7NwOIyZmZmmL35BEGgq9QhaXQntdrtRLpepKmSXUMDo6LBp6d0cDgdUVaVxmA699957OH36dEu3pWnr7qGA0dHu/UbNbN8RTNojy3LLJwEKggBBEKgqZBdQwOgknU7Dbre3dUIdXSZ1rt29XLTbujsoYHSgqioCgUDbdaXHxsZw69YtnVrVu/L5PHieb+uoC4fDgZmZGTqYSmcUMDqIxWJwu91Np013czqdVNunA9lsFmNjY23/ns/no6qQOqOA0Vir09L7sdvt4DiOLpPadPv27Y4OS6dpa/1RwGhs9zGY7bpw4QLtmWlDtVpFuVzu+Cxjl8tFVSF1NMAYY0Y3olfIsozJyUkUCoWO76NcLmN0dBQbGxsatqx3xWIx3Lt3r63Zut20+Hcj+6MejIbq1RmPguM4cByHXC6nUat629LSEjwez5HuQxAEqgqpEwoYjdSrM2pRldHj8WBpaUmDVvW2+liVFs85VYXUB10iaUBVVTz11FNYWVlpe+booPsbGhpCMpmkDZKHuHjxIjwez4FHYLRLi8stshP1YDRw0DGYnaLiYc3JsoxyuaxZuAB0vKYuGDmSjY0NxvM8UxRF8/sWBIEVCgXN77cX6PXcZDIZ5nQ6Nb/ffkU9mCM66rT0YaLRKK3R2Ec6nQbHcZqMvexGVSG1RQFzBLurM2pNkiTY7XZ6se8SDoc7WsjYKtqnpB0a5D2CM2fOIJFI6PJJWkdrNHbq1kBsIBDAiRMn4Pf7dX2cXkcB06FuzjhMTk5iZGQEXq9X98cys1qthqGhISwvL2s2oH4QrWcG+5axQ0DWtLm5yXieZ5VKpSuPpygKkySJraysdOXxzEqSJLa8vNy1x4vH48zn83Xt8XoR9WA6YET3uVqt4uLFi0gmky0dDdlrjLpk6cZlcC+jQd42tXMMppYcDgfi8TgmJib6bvDx2rVrqNVqhoyH0PGaR0MB0yYjqzMKgoBgMIiJiYmuP7ZR8vk8lpaW2j68SytUFfJo6BKpDel0GktLS0ilUoa248qVKzh27BhmZ2cNbYfeqtUqxsfHkclkDB1orVarGBoaQrFYpLK/baKAaZHZ9gddvHgRIyMjPTuNWi6XMTk5iWg0aorxj5dffnnHf0lrKGBapNW5I9VqFfl8Hvfu3Wt6VCPHcThx4kSjm777jVavtRyNRnvqkzWXyyEQCJhqcJWmrTtDAdOCarWK0dFRrKystHWwtCzLyOVyuH37NrLZLHieh8PhwNmzZxvnvhymXC6jXC5jdXUV1WoVpVIJkiRhbGwMkiRBEATMz8/j9ddfRzKZ7IkX/vz8PG7cuIFkMrnjuVZVFfl8Hvl8Hvfv34csy5Bl+dA6UvXnWBRFHD9+vHHuS6euX7/eaBtpDQVMCy5duoTBwcGWZo7K5TKuX7+OhYWFRtmSkZGRxh6Xo1BVFblcDrdu3WpsU/B4PBgcHMTPf/5zxONx03zit6teiQFAo0eWz+dx48YN5HI5yLIMURR3hIUgCIcGfj2gt4dSLpdrhLTT6Wz7+RoaGkI0Gu34iM6+Y8zyG+soFApMEISmt1tZWWFOp5NxHMdmZ2fZxsaG7m3b2NhgoVCIcRzHRkZG2ODgIEsmk7o/rtYqlQqTJInF4/EdfydRFFkkEtF8geHy8jKbnZ1lgiAwnudZNBptedFkq68HsoUCpolmq0c3NjaYy+VioiiyTCbTxZbtlMlk2De/+U126tQp9p3vfMcSxzwoisJCoRDjeZ699tprjYAOhUJdCWjGGCsWi8zv9zOHw8G8Xm9Lj+v1elkikehC66yPAuYQqVSKuVyufX9WqVSY3+9nHMexVCrV5ZYdLJPJsMcff5w98sgjzOPxdO2N2q54PM44jmM//vGP2fe//30mCIKhAc0YY4lEgvE8z/x+P9vc3DzwdpVKhXEcp8sZQL2GAuYAiqIwjuP2dJ03NzcbXfhoNGpQ65pLJBLs85//PHvkkUfYzMzMoW+YbkqlUoznefaDH/yA/ehHP2Icx5mqN6AoCotGo4zjOBaJRA4MkWg0yvx+f5dbZz0UMAeIRCJsdnZ2x/fq19+hUMgSn16KorCf/vSn7Itf/CJ79NFHWSgU6toGzd1SqRQTRZF973vfYy+99FLTN7DRNjc32ezsLOM4jsXj8T0/VxSF8Txv2h6iWVDA7GO/LnAymWSiKFryBVWpVNgzzzzDnn/+eeZwOJjT6WTJZFL3N/f28Q2Xy8Xeeust5nQ62ezsrGl6VM1UKhXm8/mY2+3e83wddglNtlDA7MPtdu+YjQmFQvu+wKxEURTm9XqZ3+9nmUyGud1uZrPZmCRJms3UVCoVlkwmmdfrZRzH7Zihqff+unncgpYO+oBxOp2Gjx2ZGa2D2WX7CXK1Wg2Tk5MYHBzsmSXisVgMN27cQCqVgt1u37GuJp/Pg+d5cByHs2fPAsCBCwLrheHu37+PUqmEfD7fWPdTXwhY/710Oo25uTkkEglLHzUhyzIuXbq0Yx0MnTh4OAqYXernf9hsNkxOTiIYDOp25q5RDluKXyqVGovTABy4pWFkZATA1jESPM9DFMV9FxJevXoVq6urSCQSba2CNqtqtYqJiQl4PJ7GCYN0vOYhjO1AmUsikWishRAEgRWLRaObpJuNjQ0miqJuf0dFUZjb7d4zUN4Ltl9uMrZ1aSgIgmED6GZGAfNAfVq6XC4zURQtsVDtqIrFIhNFUZcBV5fLZarpZz2EQqFGyNC09f7oEumB+hkrq6urmpYjNbtsNou5uTlkMhnN7rNfzqsB/rdPzev1YnR01NL7wfRAJ9pha1NcOp3Gv//9b/A83zfhAmwVGhsZGdGsTO3169dRLpf7IlyArY2ZN27cQD6fp3K/+6CAwdYg3fPPP48//elPiEQiRjen62ZnZxu7wI8in89jYWEBiURCo5aZn81mQzKZRCAQAM/zVBVyN6Ov0Yy2vLzMvvGNb+g2FmEViqIcaeypUqlYdiGiFgqFAhNFkcmyzARBsPSaKS31/RjM4OAgPvroI7z11luWXqOhhXK5jPHxcRQKhbbOrlFVFePj44hEIn19Tkr9zOb6SYQ0bd3nl0ixWAyf+9zn8Nxzz/V9uABbi+qcTifm5+fb+r0rV67gwoULfR0uAOByucBxHB555BHMzc2hWq0a3STD9W0PplarQRRFKIqC1dXVnjhuUgvtnj1LJ+7vVH8+XnrpJbz77ruGlVsxi77twYTDYTz55JOYnJykcNnGZrNhZmYGr7zySku3v3LlCkKhEIXLAw6HAx6PB3//+9+Rz+chy7LRTTKWsUNAxigUCuzrX/86O3HiBA3G7eOgs3B2o+Mj91d//n79618zURSNbo6h+rIHEw6H8dhjj8Hv9/fVJ+96Zg5z0+cwMDCNw5bV2Ww2RKPRpiVTw+EwQqGQto3sAfVe4G9+8xuqCml0wnVbKpVi3/rWt/puKnEtNsyGh8EAMGCK3WzhdwRBOHDaenl5mUmSpG0je4iiKEwQBPb73/++r4/X7KtB3np1xieeeALPPfdcYzdsP8lMD+D84hRusgWMN7ntYaVy67vOaVn8werP3+DgIID+rArZV5dI8/PzeOaZZ/Db3/4Wbrfb6OaYntPpbFSj3C6Xy8Fut1O4NOFyuSDLMiYmJrC0tNSX09Z9EzDVahULCwt46qmn4HK5DB57WUdmbhrnzg1gOgOsz03j3MAABs7NYX3XLTPTAxgYaOHPtHabFetsNhtcLteeLQRLS0vweDyaP14v8ng8SCaTiEQijcJyfcXoa7Ru8fl8LB6PN61z1A03p+pjIWBTUzEWW1tja7HhlsdGjv7YrT/OysrKjpkQRVGY3W7v2zGFdm1sbDCO4xhjjImiqHkRObPri4CpT6dubm4yu91udHO23JxiANhwbK3LD9tewDDGGMdxjT1G9UO5SOvqH2r9OK3fF5dIgUAA0Wi0UZfYTJ5+8uShPzfyEqlOkqTGGby3b99uHJdJWjMyMoJcLteop33t2jWjm9Q1PR8w6XS6cRi1Fd8c4wsMjLXwZ6HZnFDnRkZGcPv2bQBbB1Q5nU7dHqsX1V97ABCJRBAOh6GqqsGt6o6eDhhVVREIBBr7QczYg7GCeg9GlmU4HA7aWtEmSZIgyzJqtRocDgdmZmb65mCqng6YWCwGt9vdeEPIskxTqx3gOA61Wg2ZTIYCukPbLzN9Ph+y2ey+1Rp6Tc8GTH1aur6UvVQqged5g1v1P+vvvwMAeOf93RPTuj4q3n/wf+0+LM/z+MMf/oDTp09r3qp+wPM8SqUSgK3p/36Ztu7ZgAkEAohEIo31LmYKmMz0AE757wAA7vhP7bv+RYcHxcDAKfgXAWAR/lPtDQzzPI/19XU6N6dDJ06cwL179xpfu1wuqKqKbDZrYKv015MBI8sySqXSjtW6ZgqYPQO3b8/g8LkkTR70SAPDp0+fxl//+le6xOyQIAh7jm6IRCI9PxbTkwEzOTm55+BpVVXx0EMPGdQi63M4HPjYxz5GA7wd2n6JVCcIAiRJQiwWM6hV+uu5gLl27VpjvcF29+7do+79EX3iE58wugmWZbfbUavV9nw/GAz29D6lngoYVVURDof7svSI3nqhrrQZ1U/Aa/UEQav5uNEN0FI4HMb09LSluvGxWAw3btwwuhlN1Wo1/Oc//zG6GZbmcDhQrVb3vD59Ph9GR0d7chlFzwRMvTpjoVAwuiltcblclnhRybKMV1991ehmWJrNZtt3Ba/NZmtUhdSyhK8Z9EzA7J6WtgqO4ywxNlStVmkMRkdOpxMLCwtIp9M9Vbq4J8ZgcrkcarXaof8wBw2ykdaoqgpFUYxuhqWVy+VDP0x6cZ9STwRMfbf0YY4dO0YBQ0yN53lIktR24Tszs3zAxGIxSJLUdBzD4XDg/v37XWpV73nvvffw0UcfGd0My1JVtaXL90gk0lNVIS0dMLVaDQsLCwgGg01vy3FcX2wu00upVMJ///tf6gV2qNWV5DabDcFgEOFwuAut0p+lA6adaen9lmqT1pVKJTz22GMU0h1qNv6ync/n65mqkJYNGFmWkc/n4fP5Wrq9w+GAqqr0CdyhcrmMr371q3uWu5PWtLsXLh6PNy18ZwWWDZhwOIxgMNjWtDT1YjojyzJ4nsfXvvY13L171+jmWNLdu3cb9ZFaIYpiT1SFtGTA1J/0dtcL1M9GJe2pH5MpiiLy+bzRzbGkfD4PURTb+p14PI5AIGDpaWvLBcxR9hu5XC5LLMs3m1u3bmFsbAyiKEKWZUu/4I1QH7dqd0FlfZ/S1atX9WhWV1guYObn5yFJUkdnuwiCgHK5TOMwbVBVFbIsQxRF2Gw2CIJAvZg2HeUs6NnZWUvvtrZUwOw+BrMTLpfL8te13ZTNZiFJUmOsiy4z21fvAXbC8sdrdr8UU+fq1RmPYnl5mUmSpFGLep/L5WKpVKrx9fZKhaQ5rSphWrUqpGV6MO1OSx9EkiSUy2Vaz9GCarUKWZZ31EGqb86kXkxrrl+/rkktdKtOW1smYFrZb9SqmZkZzM3NaXJfveygN4fH48HS0pJBrbKWpaUleDyeI9+PZatCGt2FakUqlWIul0uz+1MUhXEcxyqVimb32WsOe47o+WuN1rWoK5UK4zjuyJdb3fR/L7/88stGh9xhVFXFd7/7XaRSKXzqU5/S5D4//vGtY3DefPNNKoN6gMuXL2NsbAzf/va39/yMnr/WXLp0CTMzM5pVs6i//n/1q19Z53k3OuGaiUQibHZ2VvP7VRSFCYLAisWi5vdtda18UtLzdzi9JhMURWE8z7ONjQ3N71sPpg4YvbuEWl969Qq/38+i0WjT29HzdzBBEFihUNDlvq30vJt6kFfvYzBdLhfK5TLtT9pGlmXkcjn4/f6mt6Xnb3/pdBocx+l21rKlqkIanXAH0XqA7CC0Lman3etemqHnb6duXTp26/1xVKbtwexXnVEPkiSB4zjrTf/pIJvNQlXVtjaRSpIEu91Oq6MfOMpWlnZYpiqk0Qm3n0Qiwbxeb9ceT1EUJoqibtfMVlAsFpkoimxzc7Pt393Y2GCCIHT0u72k289DpVJhgiCYermA6QLGqDUWGxsbTBRFU/9j6WVzc5OJonikbn0mk2FOp1PDVlmLUbNq0WiU+f3+rj5mO0wXMLOzsywSiRjy2MvLy8zpdFpqIZMWnE4ny2QyR74fs7/Y9dTu2JVWzN77HmCMMaMv0+rK5TLGx8dRKBQMK6A2Pz+Pu3fvIh6PG/L43XblyhUcO3YMs7OzmtzfxMQELly4ALfbrcn9WUF9rapRa1az2Szm5ubMWRXS6ITbzqhPgd202LVtBclkkrndbk3vU1EUJkmSJXf+dsIsa1LM8t7ZzTQBY6bpTkVRmNPp7OmQSSQSzOVy6XI52C/jWcVikQmCYIpLajO1ZTvTBIyeKx875fP5mM/nM90/2lH5/X7m9Xp1/XvV12mY7d9UK8vLy0wQBFMt2W91BXY3mSJgzDw4GI/HmSRJPfFpvLm5ySRJ6tqLsN6TSSaTXXm8bolGo0ySJNNNy5txl7vhAbO5ucl4njfVk7LbysqK5T+N6z2K5eXlrj6uoijM7Xab9gOkHVb4u8Tjcebz+YxuRoPhAWPGbt1+KpUKE0WRJRIJo5vStmQyySRJMrQ7H41GmcvlMt2nfqsqlQqTJMkSvTEzfRgaGjCFQoGJomiZMQ5FUZjX6zWkJ9zGYGkAAATvSURBVNCJ+sC52+02xRs7lUoxURQt8dxtl0qlmCAIlpkZW1lZYaIoGt0MxpjBAWPWqbVmCoUCkySJOZ1O03xSbFcsFpnL5WKSJJnuzVwsFpkkSczlcpn+LJmVlZVGW818Cb8fs7y3DAsYs6wfOIpMJsMEQWBut9sUswmVSoX5fD7G87wpXlyHSaVSjOd55vP5TPfm3djYYC6Xy5K9rTqzHK9pSMD02mloyWSy8WYxokdTLBaZz+djHMdZbu1OPB5nHMexUChk+GVcpVJhfr+fcRxn+oBuRSgUYqFQyNA2GBIwZp6W7pSiKCwejzNBEBjP8ywajeraq9nY2GDxeJzxPM94nmfxeNzwT6tOKYrCQqEQ4ziO+Xy+rn/wrKysMK/XyziOs8SEQ6vMMG3d9YCpVCqM53nDP630VCwWG5+EHMcxr9fLksnkkd44xWKRJZPJRk/FqDejnjY3N3eEZjQa1a1HuLKy0gi1+uygVQP6MK1vB1ljazen2PAwGPDgz/Awm7q5xhi7yaambnb0+G1vdhwYGDjgJ8MYHn4aP1m6jPGTJw/8/UuXLmFwcPDIBdSsolwuI5fL4datW5BlGaVSCYIgwOFw4OzZs4f+7urqaqP4Gc/zEAQBIyMjcDqdbRdSt5pSqYSFhQXkcjlUq1VIkoSzZ8826gPZ7faW76teaC+fz2N1dRW5XA48z2NsbAxer7fnn8uhoSFEo1GIorj/DdYzmPacx+KdYUzdXMLC+IP37/o65l71wL94BxiOYe3tGRz8zt5f+7up1+cwfcqPxambYAvj29o4B895P+4AmLq59r9GbiPLMiYnJ1EoFNpsZm+RZRnVarVpEXlRFOFwOHQ729UqqtUqcrkcVldXIcsyZFmGqqoHv2G2yeVyjWqUoiji7NmzjVP4+sXh77sMpgfOYxHDiK29jZl9EiQzPYDz73QrYOoN2hUwAID1OZw75ccdTOEmW8Cun2J0dBShUAiSJLXZTEJ2UlW1aUADoNfaA5OTkxgZGYHX693x/fW5czjlv4Ph2Bre3i9dAAAZTJ97H5c7CJiPd9Tag5x8Fi8M+3Hnzjt4fx3Y3olJp9MolUrI5XJU15h0Db3WtthsNly5cgVut3vbWUsZvOq/A2AYLzx7WHSMw/V0GmuAwQGDNbx7BwCexpO7WsJxHKanp7V9OEJIS44fP46ZmZmd31x/H+8A2O/9utv4wkJHj6tdwKxnMOc5j0UAw7HLey6P6oNzhBCTWHsXd3R+iM4DZvE8BhZ3f3PXKDQhpK91Xhdp6ibY1joaMMawtnYTsSlg8fwpDJybhglPByWEbDfuwhQAYGvMVA+aFV47eXIcMwtv4+YUgDuLOD9NEUOIuY3DNQUAd/DGm/okjOaVHU99eXjrf955HzqFIiFEI+OXYxgGcMfvwdyBb9h1ZObmOroq0Txg1t59MGz09JNtT2kRQrrs5AzevjmFYdyB/9Q5TGfWd3QM1tczmD7nwfvPzuyZuGlF+wGz/v7//nfH99eRmT6H84sAMIzY5U6aQwjpuvEFvL22hptTwDvnT+HUwAAGBgYwMHAOnleBy2/vv8K3FRruRQIwPIzhp1/ATy7PgCaSCCFtT1O3vbOAENK3NB+DIYSQOgoYQohuKGAIIbqhgCGE6IYChhCiGwoYQohuKGAIIbqhgCGE6IYChhCim/8Hm+mo/sISZjQAAAAASUVORK5CYII=)
In any equilateral
, three circles of radii one are touching to the sides given as in the figure then area of the
is
![](data:image/png;base64,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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
![](data:image/png;base64,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)
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.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANMAAADtCAYAAAAld0AEAAAgAElEQVR4nO3deXzU1b3/8df3O/tkJpN1sm8ESAKJYQuBBCFQqDtYF1ywloe7FqlW29724a/V3nptba/eXmupWi+1WlRo6xXcWBQUChGIIYGQhSCE7BvZJjPJbN/fHzpzRVmSEJgs5/l48AeTycyZybzne76fc77nSIqiKAiCcN7kQDdAEMYKESZBGCYiTIIwTESYBGGYiDAJwjARYRKEYSLCJAjDRIRJEIaJCJMgDBMRJkEYJiJMgjBMRJgEYZioA/nkiqLg8XgY6FxbSZKQZRlZFt8BwsgTsDB5vV7sdjv79++nvb19QL9jsViYNm0aoaGhqFSqC9xCQRicgIVJURROnjzJk08+SUVFxYB+Jy4ujhdffJHg4OCAh8ntdtPV1YXRaESv1yNJUkDbIwReQMOkKAoul4u+vj7/7U6nE4fDgcfj8X9QfVwuF16vd9DPM1hnC4bT6aSvr4+2tjb+/ve/k5mZyWWXXRbwcAuBJwXq4kBFUXA4HHz22Wd0d3f7bz98+DDPP/883d3d3HfffeTm5qJWf5F5o9HItGnTCA4OHvB5k91uR1EUtFrtgO5/tvMyr9dLdXU177//Pq+88gqVlZX86le/YtWqVWg0mgE9vjB2BezIJEkSer2enJwc3G43iqLQ3t7Ohx9+SHNzMy6XiwMHDnDzzTczYcIEAFQqFRqNZkBdKpvNxrp169i6dSsejwdJknC73edsU1BQEPfffz9z5szxh/irP/d6vcTHx6NWq3G5XOd8TGH8CGg1T5ZldDodWq0Wj8fD4cOH2bZtGw6HA4DPPvuMt956i0cffRS9Xj+oKp7b7aa6upqPPvoIu92OwWDAYDCctTvmcrnQarXceOONeDye04Zp4sSJGAwG8vLyOHjw4NBeuDAmBTRMPl6vl87OTp555hkqKyv9tzc1NbF+/XquvPJKMjMzTzl/OheVSkVKSgo6nY6+vj4yMzNZuHAhRqPxjL+zc+dOdu3aRX9//xnPtdRqNRaLhQkTJogSvXCKERGmkydP8uyzz1JcXIzL5TrlZzU1NfzHf/wH//3f/01sbOyAP8AajYbJkydjMBjo7u4mJCSElJQUzGbzGX+nvLxcVOWEIQv4V6vD4WD//v38/e9/p6en5xvVOofDwdatW3nrrbfo7Owc8OOq1Wp/l8xXVNBoNGi12jP++3q3ThAGI+Bham9vZ926dRw9ehSXy4UkSf6jg++Ev7e3l1dffZXi4mI8Hs+AHlelUhEXFzeoyp8gnI+Afsq8Xi9vvvkm27Zt8x81NBoNKpUKtVp9ypGksrKSDRs2YLPZBjTWJEkSarWahIQEMQYkXBQB79fk5+eTmprqP1dqbW1lzZo12Gw27r33XlJTU4EvwmG1Wgc92yAxMVF034SLIuCl8Tlz5pxy29GjR/nHP/6BSqWioKDgGz8frISEBBEm4aIY858y3wCrz9kmfIiVooXzMebDpNPp8Hg82O122trasNvtZ7yvzWYTxQphyMZ8mNRqNTqdjsOHD9Pc3HzWOXRdXV3ExMSgUqnEeJMwaGM+TGazGbPZTGVlJZIkYTQaz3j0CQoKIiMjA7PZfNYw+Wa8C8JXjfkwTZ8+nXvvvZeHHnqI1atXc9ttt2EwGE57X9/g7rnm8Hm9Xvr7+y9Uk4VRasyHSa/XExcXh9FopLW1FYPBQEhIyJAeS1EU2traKCsro7i4GIvFQk1NDWVlZaSkpGAymcSY1jg25sMkSRJhYWGYzWbq6+vp6OgYcpjgi7mCtbW1zJkzh2nTphESEkJ1dTWSJDF16tRhbLkw2oz5MAGEhoZiMploaGigvr6elJSUIT2OJEnMmjWLWbNmDXMLhbFgXNSBLRYL8fHxNDU10dDQEOjmCGPUuAiTXq9n+vTpdHV10dTUNOh1JARhIMZNmHJycvB6vdTX1/svkxeE4TSuwqTX62loaMDpdIowCcNuXIRJrVYTHR1NWFgYTU1NIkzCBTEuwiRJEhqNhsTERFpbW2lraxPnTcKwGxdh8klNTaW/v5/CwkKxRJcw7MZVmNLS0vB4PHzyySciTMKwGzdhkiSJxMRELBYLn332GX19feK8SRhW4ypMKSkpxMTEiPMm4YIYV2FKSEggISEBt9tNQ0OD6OoJw2rchAnAYDCQlJSEoijU1tZ+Y8FLQTgf4ypMkiSRlJSELMt8/vnnZ72EXRAGa1yFCf5vgZVDhw7R1dUV6OYIY8i4C5PVaiUlJYXy8nIRJmFYjbswmc1mZs+eTVNTE83NzQNeblkQzmVchikvLw9FUSgvLxcVPWHYjLsw6fV6MjMzMRgMVFZW4nQ6A90kYYwYd2FSqVQEBQURHR1NdXU1nZ2dYiaEMCzGXZjgi43QYmNj6ezs5MiRI4FujjBGjNswxcfH09PTw4EDB8SRSRgW4zZMGRkZKIrCoUOHxBw9YViMyzCp1WqysrLQ6/XU1dXR29srAiWct3EZJo1GwyWXXILFYqGjo4POzk4RJuG8jcsw+VZ5TUlJobu7m9bWVjHeJJy3cRsmlUpFdnY2/f39/osFBeF8jMsw+WRnZyNJEtu3bxczyIXzNq7DFBcXR1xcHJ988gk2m02UyIXzMq7DFB4ezowZM2htbeXEiRNi0qtwXsZ1mCwWC9nZ2f5Jr+LKW+F8jOswGY1GkpOTCQoKorKyUuwGKJyXcR0mgLCwMMLDwzl27BgnTpwIdHOEUUyEKSyMuLg46uvrxaRX4byM+zAFBQUxc+ZMWltbqa6uFjMhhCEb92EyGo0sWbIElUrFsWPHcLlcokQuDMm4D5NWq2X27NmYTCZqa2txOp3i6CQMybgPk1qtJiIigtTUVP9u7GK8SRiKcR8mn7S0NBwOB//617/EeJMwJCJMX8rMzMTtdvP++++LRVaEIRFh+lJiYiKRkZEUFhZit9tFEUIYNBGmLyUlJZGUlERrayuNjY2iCCEMmgjTl+Li4khNTUVRFOrq6sTFgsKgiTB9SafT+XfIOHr0qLhYUBg0EaYv+bab0Wg0VFVV0dHREegmCaOMCNNXxMbGEhQURGlpKS0tLYFujjDKiDB9RWhoKHPmzOHYsWO0traKip4wKCJMX2E2m1m8eDFOp5PKykpRhBAGRYTpK0wmEwUFBRgMBg4dOkR/f784OgkDJsL0FSqVitDQUOLj4ykvL6etrU2ESRgwEaavkCQJtVrNpEmT6OzsZNeuXWLwVhgwEaavUavVTJkyBafTySeffCLOm4QBE2H6GrVaTU5ODiaTicOHD2Oz2cTRSRgQEaavUalUTJs2jejoaDo6OmhtbRVhEgZEhOlrZFkmPDycqVOn0tPTw7Fjx8QSYMKAiDCdhizLZGdn4/V62b17t1iHXBgQEaYzyMzMJCgoiC1bttDV1RXo5gijgAjTGYSHh5OTk0NlZSXNzc3ivEk4JxGmMwgLCyM/P5/+/n5KS0tFiVw4JxGmMzCbzf6uXllZmShCCOckwnQGvq06IyIiqKio4PPPPw90k4QRToTpLMLCwpgwYQJNTU2UlJSIeXrCWYkwnYXRaGTBggV0dHRQXFyMoigiUMIZiTCdhcFg4JprrsFkMvH555/T19cnwiSckQjTWWg0GiZNmkRycjI1NTU0NzeLqp5wRiJMZyFJElqtlpycHGw2Gx9//LGo6glnJMI0ANOmTUNRFP72t7+JqUXCGYkwDcCECROYOHEixcXFnDx5UsyGEE5LhGkA4uPjSU9Pp7e3l2PHjoktZ4TTEmEagMjISKZMmYIsy3z++eeiCCGclgjTAEiSREJCAlqtlkOHDtHa2hroJgkjkAjTACUmJhIaGkpZWRl1dXWBbo4wAokwDZBvtdfq6mpqamrE4K3wDSJMAxQSEsJtt90GQElJidiVXfgGEaYB0ul0zJ49m/DwcIqLi7HZbCJMwilEmAZIrVZjNptJS0ujoaGB4uJiUSIXTiHCNAiSJJGRkUFPTw9vv/222JVdOIUI0yDIsszcuXMJDw9n//79oqsnnEId6AaMJr4lwGJjY6moqKCxsZGwsDDUavE2fp2iKLjdbpqamjh69Citra2o1WqsVitJSUlYrVa0Wm2gmzmsxKdgEGRZJi4ujqysLIqKijh27BiTJk0SYToNt9tNbW0tv//979m9ezctLS3IskxERASzZ8/mkUceIT4+fkwFSnwKBkmSJLKzs/F4PGzfvp3c3FyMRmOgmzWieDweGhsbufPOO3E4HMycOZPQ0FD27t3L4cOHqaqqoquri1/84hdMmjQp0M0dNiJMQ5CRkUF8fDzbt2/nvvvuIzo6GkmSAt2sEaO/v5/i4mKmT5/O5ZdfTlpaGgaDgfr6ev72t7/x2muv8eGHH7Jo0SIRpvEuIiKCBQsW8NJLL1FVVcXkyZNRqVSBbtaI4XK56O3t5eGHH8ZqtaLT6YAvFvYMCwuju7ubN998k+LiYrxeL7I8NupgY+NVXGSRkZFcdtllqNVq9u7dK2aRf41er6egoICYmBh/kOCLHUYiIyO56qqrMBqNdHZ2jql1NUSYhkClUhEXF0d4eDhFRUU0NzcHukkjikajISoq6rRHa0mS0Gg06PV6oqKi0Ov1Y6aLLMI0BLIsExoaSmJiIo2Njezbty/QTRpRZFlGpVKdNiT9/f3U19djsVhYtGjRmOnigQjTkBmNRrKysmhra2P37t3iUvYBUBQFm83G3r17WbJkCZmZmYFu0rASYRoig8Hg7/sfOXKEvr4+EahzcLvdHDlyhH379rFixQqio6MD3aRhNaRqnsfjobu7m6NHj6LRaMjOzga+qOL09fVht9vxeDzfOLGUZRm1Wo1er0ev16PRaM7/FQSIRqNh1qxZWK1WampqaGtrIzo6ekwNQg63mpoa3njjDb73ve+RkpIy5t6rQYdJURT6+/v55JNPeOaZZ5gyZQpr1qwBvgjZzp07OXDgAMePH8dms6FSqQgODsZgMKDRaIiIiCA0NJTc3FxiYmIwmUyj8k1VqVSEhYUxc+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.
![](data:image/png;base64,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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
![](data:image/png;base64,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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
![](data:image/png;base64,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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
![](data:image/png;base64,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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
![](data:image/png;base64,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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
![](data:image/png;base64,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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
![](data:image/png;base64,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)
To an observer B, when the block is compressing the spring
physics-General