Physics-
General
Easy
Question
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. Net torque on the rear wheel of the bicycle is equal to
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)
- zero
- 16
- 6.4
- 4.8
The correct answer is: zero
Related Questions to study
physics-
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant, and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. The tension in the upper portion of the chain is equal to
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)
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant, and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. The tension in the upper portion of the chain is equal to
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)
physics-General
physics-
A uniform bar of length 6 a & mass 8m lies on a smooth horizontal table. Two-point masses m & 2 m moving in the same horizontal plane with speeds 2 v and v respectively strike the bar as shown in the figure & stick to the bar after collision. Total kinetic energy of the system, just after the collision is
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)
A uniform bar of length 6 a & mass 8m lies on a smooth horizontal table. Two-point masses m & 2 m moving in the same horizontal plane with speeds 2 v and v respectively strike the bar as shown in the figure & stick to the bar after collision. Total kinetic energy of the system, just after the collision is
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)
physics-General
physics-
A uniform bar of length 6 a & mass 8m lies on a smooth horizontal table. Two-point masses m & 2 m moving in the same horizontal plane with speeds 2 v and v respectively strike the bar as shown in the figure & stick to the bar after collision. Angular velocity of the rod about centre of mass of the system is
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)
A uniform bar of length 6 a & mass 8m lies on a smooth horizontal table. Two-point masses m & 2 m moving in the same horizontal plane with speeds 2 v and v respectively strike the bar as shown in the figure & stick to the bar after collision. Angular velocity of the rod about centre of mass of the system is
![](data:image/png;base64,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)
physics-General
physics-
A uniform bar of length 6 a & mass 8m lies on a smooth horizontal table. Two-point masses m & 2 m moving in the same horizontal plane with speeds 2 v and v respectively strike the bar as shown in the figure & stick to the bar after collision. Velocity of the centre of mass of the system is
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)
A uniform bar of length 6 a & mass 8m lies on a smooth horizontal table. Two-point masses m & 2 m moving in the same horizontal plane with speeds 2 v and v respectively strike the bar as shown in the figure & stick to the bar after collision. Velocity of the centre of mass of the system is
![](data:image/png;base64,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)
physics-General
physics-
A uniform triangular plate ABC of moment of mass m and inertia I (about an axis passing through A and perpendicular to plane of the plate) can rotate freely in the vertical plane about point 'A' as shown in figure. The plate is released from the position shown in the figure. Line AB is horizontal. The acceleration of centre of mass just after the release of plate is :
![](data:image/png;base64,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)
A uniform triangular plate ABC of moment of mass m and inertia I (about an axis passing through A and perpendicular to plane of the plate) can rotate freely in the vertical plane about point 'A' as shown in figure. The plate is released from the position shown in the figure. Line AB is horizontal. The acceleration of centre of mass just after the release of plate is :
![](data:image/png;base64,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)
physics-General
physics-
Two identical uniform solid spherical balls A & B of mass m each are placed on a fixed wedge as shown in figure. Ball B is kept at rest and it is released just before two balls collides. Ball A rolls down without slipping on inclined plane & collide elastically with ball B. The kinetic energy of ball A just after the collision with ball B is :
![](data:image/png;base64,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)
Two identical uniform solid spherical balls A & B of mass m each are placed on a fixed wedge as shown in figure. Ball B is kept at rest and it is released just before two balls collides. Ball A rolls down without slipping on inclined plane & collide elastically with ball B. The kinetic energy of ball A just after the collision with ball B is :
![](data:image/png;base64,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)
physics-General
physics-
A child with mass m is standing at the edge of a playground merry-go-round (A large uniform disc which rotates in horizontal plane about a fixed vertical axis in parks) with moment of inertia I, radius R, and initial angular velocity
as shown in figure. The child jumps off the edge of the merry-go-round with a velocity v with respect to the ground in direction tangent to periphery of the disc as shown. The new angular velocity of the merry-go-round is:
![](data:image/png;base64,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)
A child with mass m is standing at the edge of a playground merry-go-round (A large uniform disc which rotates in horizontal plane about a fixed vertical axis in parks) with moment of inertia I, radius R, and initial angular velocity
as shown in figure. The child jumps off the edge of the merry-go-round with a velocity v with respect to the ground in direction tangent to periphery of the disc as shown. The new angular velocity of the merry-go-round is:
![](data:image/png;base64,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)
physics-General
physics-
A uniform solid sphere rolls up (without slipping) the rough fixed inclined plane, and then back down. Which is the correct graph of acceleration 'a' of centre of mass of solid sphere as function of time t (for the duration sphere is on the incline)? Assume that the sphere rolling up has a positive velocity
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)
A uniform solid sphere rolls up (without slipping) the rough fixed inclined plane, and then back down. Which is the correct graph of acceleration 'a' of centre of mass of solid sphere as function of time t (for the duration sphere is on the incline)? Assume that the sphere rolling up has a positive velocity
![](data:image/png;base64,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)
physics-General
physics-
Two identical uniform discs of mass m and radius r are arranged as shown in the figure. If
is the angular acceleration of the lower disc and a cm is acceleration of centre of mass of the lower disc, then relation among
& r is :
![](data:image/png;base64,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)
Two identical uniform discs of mass m and radius r are arranged as shown in the figure. If
is the angular acceleration of the lower disc and a cm is acceleration of centre of mass of the lower disc, then relation among
& r is :
![](data:image/png;base64,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)
physics-General
physics-
Figure shows an arrangement of masses hanging from a ceiling. In equilibrium, each rod is horizontal, has negligible mass and extends three times as far to the right of the wire supporting it as to the left. If mass
is 48 kg then mass
is equal to
![](data:image/png;base64,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)
Figure shows an arrangement of masses hanging from a ceiling. In equilibrium, each rod is horizontal, has negligible mass and extends three times as far to the right of the wire supporting it as to the left. If mass
is 48 kg then mass
is equal to
![](data:image/png;base64,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)
physics-General
physics-
A uniform thin rod is bent in the form of closed loop ABCDEFA as shown in the figure.
The ratio of moment of inertia of the loop about x-axis to that about y-axis is
![](data:image/png;base64,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)
A uniform thin rod is bent in the form of closed loop ABCDEFA as shown in the figure.
The ratio of moment of inertia of the loop about x-axis to that about y-axis is
![](data:image/png;base64,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)
physics-General
physics-
In the figure shown, a small solid spherical ball of mass 'm' can move without sliding in a fixed semicircular track of radius R in vertical plane. It is released from the top. The resultant force on the ball at the lowest point of the track is
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)
In the figure shown, a small solid spherical ball of mass 'm' can move without sliding in a fixed semicircular track of radius R in vertical plane. It is released from the top. The resultant force on the ball at the lowest point of the track is
![](data:image/png;base64,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)
physics-General
physics-
A ball of mass m moving with constant velocity u collides with a smooth horizontal surface at O as shown. Neglect gravity and friction. The y-axis is drawn normal to the horizontal surface at the point of impact O and x-axis is horizontal as shown in the figure. About which point will the angular momentum of ball be conserved.
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v3VO8gttk/WWSMDyQ0UlH0kx1hBr7ztuY5/ZwIt0dKNKRyQZ0HQp+KFMgr3337rdMaukhopGJhnk0pOrRvk2jrOiY6UgFSRmpWrSxpUryo+TqhjIRCKhbg2bSP5EC2X0pM6p4fiZJUgMVhgnGTJ31WWr7eRHeGCEWEOqnwqhJKluKFpDJmdJjTmriRaEnlAscI9Rzy5cohX61d47SGDkKZVNTQ/37rVk0O7NW9my3U4yDRkwqQ6MhmYC8lTaLbA8V2FaKLFy/o7pIY8xTNjAmhSCq8s2w/S9AzG08cPWr3avbCksoBC5Ij3huq3sGGdWtr4ZnYAPGL3bt01rJaJGHWq11T3hs8yPn2eoQiqbBD77/rX1ri4Ptt8bMJQCjDksoHZo58r+XQsKjYKCNMpnLm9Gm1fgIIGzEsUGYsml3+Q4lUOHhQkb/5+it5561+cZqinpBgSRUF8GK93rihOjEGv9s/qJ6sju3bqufRBXGKr2XPIsui2bMrVEj18aIFmtdWskgh+f03uwFdTLCkigbYVe+PHa3l0apVrih7995czOGNQNgONePXrlktGzdukLmzZ+o2sNHtfBLfpCKlhrqCXTt31HIGu3bujPNN1BIaLKluAFSdgnlyaWr/px/ffgJk+9YtJX+unDJ2dJhMMLbJW3176wzATBAV4otUbBy3etVKKWCevU+vHnLp8mXdtsbixrCkugmcPHHSkKGVJHv2Kenbq+dtRLxf043JcIS4wE7Bpf/JxwudlsiIL1KRQUsKTvHCBTXQ2eLmYUl1k0DlIVrg5ZeSScVypeUHYwv9E5CRSiS+u/k4SXts0sbWolEhrklFQh+bye3evUujJO7U3UNiE5ZUt4hvN22SEmaQp3s5RbTVe2IChU7ISO3VvasSpXXz12X0qJHOt9cjLkl14MABKVuyuEZHfLxwvtNqcauwpPoHIC2cmuXscMia09lbjCSg6lOPLp10oXnunNkxlmh+b8ggKVGkYKySiusfPnRIVq1cIdUqVZBP77DiOXENS6rbwKwZ0yStmbFwM2/+7tYi3v/4/XfZ56kFf+HCBd2tgkgLtozROgt1a0n2LBmlSoWysUYq9gluVL+O1KhSUVW/hF6DPRRgSXWboN53mRLF1PU+ZfKkW3Y3b1z/jXoAKVucNlUKyZcrp5QpXlRJVbtGNd2WtEqFcrFCKipXDX53oFYC/mLpEqfV4nZhSRUEnD93Tnr16CovPPuUtGvdUr2FNwKLvtRsoEQAm5f16NpF1S5mL28eUmzYVBQm7W7Uz5lmpmU/p0MH7+xNHuIallRBxMIFH2l5NNa1UOWiwr69e6Vbl466cXj5MqVk0YL5Me6fRHpKMElFZi618R669y4JG35r9T4sbg6WVEEGNe2oh5Hqxed1gfeKp4b3ls3fqdcQVXHC+2OjrMXhRzBnKnbROHbsmO4j/P7YMdZ+iiVYUsUCMPj7v9VPvYNs/0MsIRHpRFKwg/yt7MUbDFKd/fWsRsKnMzbb6pUrnVaL2IIlVSxi8WefSraM6dUJwQxVt2Z1OXWLmz7fLqlINcF+w24bNnRwUG0zi6hhSRXLoJBkrepV5MG7/yP9337Tab15/FNSYTtNnjRBiXzgwH45fcpGRsQVLKniANhOw4cOkZeeT6Ku8gOGaDeLf0qq6VM+1A3yKpQpHb4NkUXcwJIqDrHiy+VaXDJrhnSy+NNPndaYcaukYmZkS1ecIgP7vx1t8qNF7MGSKo5x5PBhaVC3tryQ5Cl5+82+N9w1/VZIhQ2XI0sm6dCujfXsxSMsqeIBJECGjRyumcVESxARHh1uhlSEOP12/rz06dlD00rYDMAi/mBJFY/4et1ayf1qNsmYJrV8NG+u0xoZMZEKzx6LzATcYkMxOyXmIpahAkuqeMaJ48d1Lev5p5+Qnt266IzjRUykQpUkNwsHyBdL425PW4uYYUkVAiCwlQiLZM89I2VLFJft329zvhEZ/O4AKVWssKp4LvidHVBI1yCq/Z/shGIRe7CkCiFs2PCNFMibS15JmVxmz5qhZMODx87r7lae+/ftkxpVK0m2TOnlh+3fa5vFPwcBzGy+HpNj5/jxY/K5EWJewUaEzDfRlBmwpAoxnD59Stq2bC4vJ0+mqR+Z070iSZ56XOrUrC579+yRbzdu0NhC3PN//x27lXQTAz5euECefuxhLWrq1mL0g4DnsiWLqXoOtmzZLEUL5Vdva1SwpApRkG7/8H33yFOPPiRJnnxM7v/Pv6RsqeLGtopsc1ncHpih2M2e4qlpU70kkz6YIJcuXXS+jcDHixZK6peSycQJ45WAlOxGk4gKsUaq/Xv3ys4dO+TgwYO6NSX1yjGsaWNnQz7TTsETft+2dWt4m7YfOqg1E/zteo4fthupsidS+89HjmgUNvX5/O2UJkZtctuxRUjB2PHDD+HH8Z9z79m929xj5HbOwT3v4Hmcc/CTeyeujn2I3Xb3edgK1XtN2n8yv2MvueflP/fCs+w09+Ieyw79VIBFgkIoAnMfuf8eKWakI/fBPXqvyU/Oz3OSqh9+Te3D/aom0u5ek43YuJ73PWi7eU6e3dvOT+6R3eS5bsS5D+nzcU3vOTiWClHbt20LPLOnnT7nHYW3/2TaTZ/TJ96+4ifvgs0PvM/DT87DmPA+D8fuNve2a+cOPafbzvPQ5n8erk/hHu6H87FAvmrFCq3H+NiD9xsNoapWkMK76gWbMJD/1rVThxjr7ccKqRjYBHBiYKOqVCpXWgsxFi2YXzdcq1CmpGkro/+piUCJrtw5suuaDZWKKpUvo8cjPciEJZ2cdo5l7152nac4Pn+v7ZUrSvHCBbR+XsS5S0t1087mbtTsq1jWnNe0Vzbn4n+2jOmkUN7c4efmZ2VzXdStogXzhd+L/jR/myntK1qui+M4D/dH3lT2zBmc60U8D8+eI2sm/Vvug3buJVf2LBpc656bvkGtyPDKy/pcfHafk2h2iETe00P33S3/NT+pZFs4Xx5zfKrw59e+qlTeHJ9N3fM8A+2ci+vkyJJR8ufOqZ/d90BxF/qwdPGinvZyeg/sj1zOzIiB9sBzFimQT/uLQedek3vk2akEFfE8ZfR3ji2ofRvxnPwd74ExEOjDwPvBXqRdz6v/A+30LcHIEe30YQUtyU3fcg8cyzXYfN19P1yLa3Lf5UuXkIzmOSPGYeB5yBbQc3jOTcJoZXMuBNn//s//SHkzjiCfF5998om+h/ZtWjktUSNWSIXu2bhBXZWSpD0gMX4yv1c1N81Oez//fETbjhtddcnizyWPeTHop0ho6nPzc96c2bq9zepVK3RDZqTRCWMwNmlQT5o3aWwe+Cc9D+38r1G1snTq0M5InoN67p+PHFaJicrU/81++pn2U7+clBnTp0g+M9DWrV0dfk1smTFhI/WlY4SGt5/6Rd4xf88L+sFIVO7lqLnunt27pHSxIjJoQH91ix8x52f3C2pVMKAolEntPM5xzLSvW7tGB8ScWTNM+wltR0KiRjRpWN9I053aV7QfP35UvYHNmzSSRvWoH1FJOr3RTjas/0be7Ntb+vXuGf6c3M+a1at0cNNn9Cn3cvLECbUX8hqCkyqvfei0tzE2W32jwuz9cY/eG31z9OgRbaOCLtJc35t5TuIUK5pBx5aj7rukbxbOn2cGZw617U46fcVzTTbqU6F8uVXSY+DTfsr0IZs/MOi3bdmiNoq+H3NuhCDlBOg77o/zM1sWM0Jy+HtDwtu5T1JmCuR5TaZM+kA/0872PYMGvCOljEBg1gyMlcA1yW5GWOzeuVOvybk4pqgREqPCRuh44hk5dpfp/xavN5Hnnnxc6taqodfyqneMsQqlS2kuWrlSJTQfLToEnVRU5GHWgFBeTJ08SSWq68VyAUHwcHnBhmx1alSXcWNGOy0BMEWXMgP5oJnivSDjFslN53gxcfz7UrNaZT2fC36nlvkH5jsvqIiEJPaXX2aAsU60ZtUqpyUASkLjPPCeG5BHxSZyV69FrlVB9aVunTo6nwJg4/DGRkKigvjBgETF2/zdd/rTBYPOjzfatJbeRjXxAvWEgi7+HUU2rl8vJYoUUlXOi6VGuFFr47gREF7MnDZVhSHln11w7gZ1asmokcOdlgB4t8wIs2ZMd1oCOHb0qM5+SxZ/5rQEQB1FZrw//ohcmx0yNTTCxO+RI2KEoqZeQJTSxYvIsqWRa9FTnppF8U2bIi83DHl3oDRpVF93eXGxccMGJTezHfd0+XLEd4DnQuBwr4CyB8yAjPWoEFRSkZyHZJjwfuQtP7EvUFuQqF5QI6GcmQH8BRtHmxmjepWKmr7g4tezZ3Wahpxe8MJKFitkpHLkCq/YKcw6/muOGDZUCfun74X17tldWjYzZPAUbuH31kaqd+/a2WkJADsKlchfuZUdMVA3mXW8YBZGSiPtXFwzpGPRl8VdP1iDYnYqVqiAlDYDPW/OV9VxwcbUflAuGtIzuLyYPHGC6a/ShgwRjg2iLTjvaCOlvTh79owZ9CXN+4hMhoNGG+C+/UVhxptZFDXKvyCNcIQM3gELunZ8Q2t3eIE9g5rt35+LAp5sIvfdpk1OSwCrzQDmeN6rF2yK3sWc3wtsIdS5Ab5Um00bN+q5veuAq8z1M6dLo9kDe6Lx/i3+/FNVxzcYgQQYF7w7NrGIKnYzqKQaPnSoFor0+vNJe6CjCR71AgMVSeJ3S2JAFzGdRw1zL4YOGqjSwh+G07NbZzPwmzmfAuChWzV7XQeiFxinTP1IJi++WrtWr4lK5wUDlpnRK72v/HnFdGhDLf/sBcVaWD/yS+8zZ06rujBz+lSnJYD58+ZImeLFVCh4sdKoU+lTp5JWzV/X3xlE48eNMfZUZrV5jnqOp2gL9hFqnxfMrsVN3375xRdOSwBjRgWEFcLPC2bXpkYF9RrfDMwObduo2ukFKmMRI6z8Uhp1CUHjHbAAQhYzx+NAcIFW1bZVC1XPvKB+OzMgKrUXCNcqhsSo1F5gOjDr+vcSm2H6urwREt6dHXk/qHX+mRuHB5urR7dOxb1yfa+AB/TVuXO/RumwCBqpGLBIab/0RvdEJfCrfV06dtCp3OthgQzYEf369HJaAti6dbOee4tRhbzA3sIjhtTzglmrlDHCsXVcQG5ULQaQF0hypPfY0aOclgDYAxh7bO6syFVoqUqLc8GvalKPIjBgI3f+O0aYNDZ2oLceBTYITgK/qkkfQYZ2rSJLdUAqRxKj74cNH+a0iAww9hjS0u+lYlbo7JPeSGEECradFwgY+pZSa14wYJmlvMG5OnMbmwub+arH3kDQRTVgeZ5K5UvrrOnFp58sUmF17OgxpyWAqZMnS8WypXSXES+wx1izu3QxQqCSI4bKT9lsL1Clmbk/9wnrDya8rw6q33+/cbT/7SIopIKtGNu4gb3AlYt3Z+2ayC8SCYrdhYvTizmzZqrk9ao5nLthvdrybv/IahJkwPPjVzUxSLENPpo7x2kJYMZ0o2oakuCo8ALnBN4mv/Tu17uXSm8GkgucAKWM/o4DwAsGLAOT7XG82LhhvSO9IyIfMH5790DVbBrp3GDr1i2SOX0a+WTRIqclMiAner1rxzF7++tdLP78MykBGTyeK6Qw6goODi94ZjSL4WbQeoGEx76cMW2K0xIAz41D4PixyHYXazcITr80HzxwgNQ3M49XmlNOAKE0e2ZkVROnBWPCH8OIY4O+3bQxoHq5QLXDieOdYa6Zf66w9gKbFFOAmT8uEBRSUdDeTwb0baQXnjcvKJmMbcSL8AKPDeqgX3pPMlIOMnhLKzMY8cLUqlYlEhl4eQzYpkZ6e/V6HBu8GHRjLyA9njp/OTFsI4QBXigvOnd4Q9UyL7hO00YNpFePyI4CSI9DhIxfL1YsXy4F8+U2RIxsGwCECi737dsjzxouZhrBkCZVCvV6AWZL74Cl/0sWK3yd9J5tzsvMiPPDi/FGi0AwocZ48Xa/vprzdcVzbryGCBTu0QsGLGT40rfrJGSnDzd/G1G5lxkVYdW4fr1I7+eymenatWklHY2q6fW48W7RLt7q28dpCSCwvVFu00+Rw7RwtvCeUelcBLSfxup1jisEhVTETvkHJsbvtCkfXldnHLcsL92vJhEigvTy67aLP/tMUyS8oKMWfPSRGrVeoGLNmT3zOs8Wnkikrt8jh8OBWuZ+4LpmTcIPngeJ6gWqD0Gtfq8ZwoPj/aoM9hv9FRWmmfPgdvfbWS5QPbG36MOogLrLriJ+u5NdGv2zKGDmYfnAj9kzpsvOnTucTwHgtGC29zsh6MN5RivwRxcwS/v33IJUc2fPVhe3Fxj7OEn8eWBnz56VGVOn6tKEFzgxFi24fj8vlkiWLvnc+RQA18SjF12fxgaC6qiwuD2wlkfmrl+9dIGnq1rlCPXPIjRhSRViqF65kpQ1NiHqlhekd6R44TmZ9EFktdki9GBJFWJgjYswp7xGDRw8sL/aMAPeeUsXG1nktKXGQh+WVCEI1noIJcIBwKIjHjdqBkYVTWERerCkigEY0MTyedeYogMOlm83boy0yHm7IKQIgv15E9ePC+Ds8K9zxRZYb1q4YL5GQSQ0WFL5QN6MGy1A9AALwBT1vxHwdhJWNHTQu07L7QGvVcf2beXbTbE7qMhoZaH3ZpA7R1YNRI5tkJJDSFKh/Hk01ymhIeRIxWDivxfeRVLvukywwXVavN5YV/CvXr2mAa+s2p9z3OLe+/ADUhGBMHLYP9ue5loU58bFzI6LuKt57r/+uiJ/mRmR3+kjvxs7Knjv+WoU/cpCKYv2/mfjWv7zo46yVhUT/C53zsG5vedy2wK/R1zXPYa1vbQpk8ueXbsijYVAH0T//v3Xji+EDKlwE8+eOUPDYAjBJ57N7STiA/k8feqH0qp5U3m7Xx85fPiQfLVurS7GdmjbOlKYDYuZCz6ap4GWBHn6tw5FpSIOjqKTpCq4MWKfmFkqe6YMujjLugkBsOQIEcw5JixM742I+KgAqVhgfcvcGyEyPbp2ljf79IpkB0EQ1qi6d+6oIT0EGrtYvWqlTJ0ySe+XNIsj5u9wUrjJdV06ddBnbWdIQAgSfeSuDbJIyr2zwDlsyCBdO3JBwOr8efN0jYtNuzkPSX6AmDcWmwvkyaVrOYCNvsePG2uObaYzJf3IpnYgJlIhAPr17SWvN2qoyXzu+yBUacDbb0Wq58B7IxqEd45KSUQH77d1i+Ya7MuMnzJZUt1PmTU5jiPynf4nA4D4Sm9wMovehJ8RstWtc6dIAc28W7J5ibQgnca/5hUbCBlSzZ83V5PwCDuaYF5q4QJ5w6U+gzP580mkmek0XjgRGeQPkUpC+FKV8mV1JZ0wmTOnz0jdWtU174YIcKIdKLO8wInUYJM1NlwjcHOIebGs+pPkSCwZUQAErRK4u3r1SiUECW20ETnPgM+Y5mVZu/r6hVQWKklmpGRYz+5d9TkYHM0aN9LvcZETWEwiIYOMQZsnR3b5aF4gnIoYSfatIoKAwUxoE5sLkO7CQGDBnCgUfrYyf/v04w+rfXPx4gV9ljw5sun9EUhMUiKLrCBsxHuSJkVyjXgJBNRW0sRPno2FX/LEatWoqhER9B8BtI3q1VVhM3K4+VszY4xxotqZiaMiFcKvScN6GvvIQnjPbl01YRTVlTw1fmdgu+BZedcIPwb6i0meMc9aQyMfWLwmZSV96pTyofmdnDOEDH1FKg/nIYgWgQiI0axYppQ6c+gf+psA5gsX/tCAY6Ja6B+iRwjsJSQtpk32goGQIVVXI0mIH3OjAYg8WLRwvv5ORDhZoG4wJHZAsiRPa2AmQCoS0k/i2rKlS+SJhx8Ij3JHoSDkhsBbpHDpEkWlSsVy4WoEswCSmhhAQOQ0kQ2AFO+Chpze/CCIwSzkB6QqU7KYBue6M+y8OXM0q5n09Q/Gj9MMXwJjXTCAyZ5FxWEwEU2BZEU1unjposblEdbkBZEaxOUx03Ecwaqk2xN54qKVkegU6MR5guRngLqRIDwvSYTrnAiLPj27y7gxgWBiZn+I6Y12IauWxFBAGFlUpIKM3DskdDFz2jTNOPjll5PaB5DNBYO/YN5cmqM1ccL7Wj1q+bKlRgUOqH8QgMxfQLgbYVNeTQSB1aBOTf2dEm5ZMqQJD/u6eOGiDBo4QJMreTYEIkmVgMBr+oWk09hEyJAKlQDjlH2ccCfjLHDVMpLTkPoueAG8qF07AqE0xHoh1YlDYztPpO+lSxEeMwxxUrzxpjHovS8YoK4wgEHnN9rL+05yJDYVg8ob0zh2VJjOJH6g/vECSbBzQV4UZQL2GXK2bdlCc5C8QDVjcKHeMFCImHABIbinlV9G5BsR8kR0NwPKFQrMqqxfeaMsli9bpoG5zHYQpk2rFs43gXMguV0vHvUW2LfKBermvLmzNe+MaPdUZvYk+BdERyruhcGdwcziBcwsSTYznlBA6FRMpKKvIdA5I/BcYNNCUjezAUcR7zBsxHCdoXKbWbl504AGQKKoS3ovSD/iXbMkwd9QoYr3hoBhrPjtxWAipBwVkAiJTcIYMxN2A3izdy+N9naNWwInqTFAYRAAmerWrKYFPpBOqHNeo5WUb9QNUkdqGXXAHxRK9Haj+oEXQ0o+6idQUplZwZtCAqnI4vUjnFSeAFo8iXlyvqqzBEGhPJcXDGyip8n1QQ3ypmtw/15S/WHUGQYQyZ7etJPOZrZD7SQXyQWJmewu8uPu3Uqqvp7odGY6iOglFQQClD/j/KhMJGZih5UxM3vzpo31++hI5WKTUfdI9+ddvZLiRVW1UXtzZsukaqsL7DeXVNxfofy5NQDZhUsqljKYPQn65XiEztQPJ+ksTQYBgCiYBV7Qd8xwRPSj7mGvYa/zk3vCFvU6SIKNkCEVKhfGtovp06ao0wC9m+n/RqQiYh3jFZWQHTW8wbYtmzfVzkX6Y1tQYsoFqgGq4eiRAbuhfdtWansAalxAKuoeuEBNjIlUw4ZESP0AqbJroiH3jK3j3YyAbGPsAzx/pOd38pzXJRUODO4btRTBgLvZCwZJyhdfMHZeRIZzt84dpLiZ2emvUUa6cx0XflKhgrq2KzM2tqh3Xa6ssU/cARwdqbCbSMVw89oY0OQ/1TTvBIFEjpg3D4wkRPqFcmtKKqOOevPtXFIxl6D+PvvEo7LB4+jAxi5ibGFUbhwpZJvTRwBVun2b1jobtmjaRAWEF1zvy+WRkzeDjZAhFWnyqczgoMNRmxigDCoGRtdO7OaeKZxUeK1SG0m4xUkrYIYqV6qY7PtxT8C2KV5UVQoGMoRM/0oqI6UCyYZILHT4HmaQolLg9OAFMyuBbqadakWkoHBeEvu8UeFISX/6ByDDF2Pam8JN9Dbnwh5QQpcqruoI3kFULmL5XAlOKktLz3khFe58bENUpwfv+bfOdJAPFXPwu/1l+RfL1E4kNYZn4LyoYWlSvaTpOICiKN7sXfKZsF3dNHY8qcxq883g5D/nGWuECnlZJCOiLiHxUZcgFaklfuB9ZLbEWYRg5P5SJEuqzh3+bpiZvamY9N6QQSp0GOgEDjNTcSzVdr3R/DifMhnbhz6gxBh/y71wT/QbKjXeQQQUMxwlxRB0SxcvVgcQ61sIMgTQa9myqkdyiflbigMhjDlnbCJkSMX6C2oZs0iDunVUjXDzYkhcQyVz9WDS3pHA7gyCzUOu0cmTgSBUvketQW1gQEEu1l0A51i2ZIm6ZnkZQw1J9noyh7dv2yo9unbRTF6qJrGbhnfTgK+/+kodJX7ghUM6elMsqBPIrOfmMRGFjmeMSHPKXDEA3VkBlQRh4gKJi4MEQkMA8sRQU3uae8NR0smoPeRJAfLF8DjiDX2D8xqhw4AEzEg4b1xga9DPboIoKTecmwHPehzf1a9bSzOwuXdSKSA1Ao0ZBYdQVMCbiJu8jpmh8ASOMjP/r2cDRIEwI8xsCJnISdu6+TtVLekzMsVxTHjTVchno/8vXw60oc42bdhAPaPMqt98/bXaV+5yBc/gvm+WDOhnF2gzFMZBkDCDfxtFqkuwEVI2FUCie43u24E/+c6PuEitjgruYnKw4c/d+qeIbpGV9b0b1W9n1nI1Cj+uXImw+24VV/++agRFzOFaMT2/V72MbYQcqSwsEjosqSwsggxLKguLoELk/wAbs8ZWNmmwQgAAAABJRU5ErkJggg==)
A ball of mass m moving with constant velocity u collides with a smooth horizontal surface at O as shown. Neglect gravity and friction. The y-axis is drawn normal to the horizontal surface at the point of impact O and x-axis is horizontal as shown in the figure. About which point will the angular momentum of ball be conserved.
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass m is moving at speed v perpendicular to a rod of length d and mass M = 6m which pivots around a frictionless axle running through its centre. It strikes and sticks to the end of the rod. The moment of inertia of the rod about its centre is
Then the angular speed of the system just after the collision is
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)
A particle of mass m is moving at speed v perpendicular to a rod of length d and mass M = 6m which pivots around a frictionless axle running through its centre. It strikes and sticks to the end of the rod. The moment of inertia of the rod about its centre is
Then the angular speed of the system just after the collision is
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)
physics-General
physics-
A uniform rod of length
is sliding such that one of its ends is always in contact with a vertical wall and its other end is always in contact with horizontal surface. Just after the rod is released from rest, the magnitude of acceleration of end points of the rod are a and b respectively. The angular acceleration of rod at this instant will be
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eM17Hv7D7wVWvkE4yfxCJDYoZUJmaIHTWSfPxRGVm8aIGfOgOEdOiXHDJvxHyzDBmu2DqDRQDwiQictmRoSGmSEcIS6CjHiRPkwvnz+hzVGk3xXWLhK2j/bNe6pZIRzVOFsqVkybeL9fVd2L9vn3zatbNky5hOYpm4ggYgxHzWTbLwD5+IcMDcWF06ttfsDZkZKszTJn/lR/SmWqOXsEONIt/uXb9I209aSvJECbQ99OPyZeTbRQv1ZwDi/maI271LJ0mbMqkkjB1TxXy0htpFJRbu8IoIiN42/fyTtGnR3Nx08VUqXb5MSQ1Cz/vrI75x/bruSWAgcGgSASD0I4Bu19oRM8SOHlkqV/hILYP7ja7KVvRLxnrgJlEdnz1rhp+pexZvN7wiAh1jn40aIelScKrG0EFfbMa5GkDBih1qBM10rTmIEPqb97dv2yqtDUlRreKuffxRWVm2ZImfzT7UIrp26iCZVb8UWYobl27enFm2zmCh8IoISKTxrcuXLiXVK32s7ZQM/QoITLNgVDw3pWqN6vouuvMVuEK//LJdWjVvKkkTxNMBAg7LsMi89wf6nIcPH2lrKK6dS79UqlhhmUs3nHWT3np4HSMcPXJEVq1YIT9sWO9Rx4NKdeWK5VK54kc6x9RBhNpB1hr5ApqGdmzfJq1bOty3ONGiSNVKFWT5UiyDo+0TqLK1MzFDMofMu3hRJbaVY7zd8ClYDgwEyRCFIcEpkyaUSOHeUalFcLVGvmLbls3SslkTPfUJ6LEMK1cs80MGdjh0bt9WZeWxo0fRBqCv583zU6W2eLsQIkTgBkL7U6NKJUmdLJHegOT3yS4x+zQ4WiNfcf/+PbUMjK5PGj+2uknVKleUZcYyMFMJ4OoRQLPdk8WGCdEvlSiu6loGHlu8fQg2ERjFSCWZqdfsScP3RnxH7h6JBRYhtGME/0D+sW3rFo0ZGE1PS2eNqpXUMhDMu0CV2hEzJFWZd7lSJdQy2DrD24dgEeH8X+d0XRSpUkaxcPMTE3Rq304nUajWqE7oZ408YcvmzdK8cSMdRpwwTgy1DKuN+3b79nMy7N61Uzq0baMbQONEj6qWATGf+9AAizcfQSYCnWijRgyV/HlyqitEapXR7xt/+kmb6UNDa+Qr0B9t27pVmjZqoLokguiaxn1bsWypPHzk6K3ATdq7d7e0b/2JpHDqlz4qXVIbgDxN/LZ48xAkIhw+eFBVp8wlZdgvuwwG9uujQjx87LlzZkuhfHleORHAk8ePjWXYJM2bNJIkJl6IFyOa1K5eVVavXOknHti1c6d0bNdarQduEpKNBV/P95gmtniz4BMRdIDvoYOq7GTKBMUrmuaHDxmsuw1AUOcahTbY0dCkQX1N6dLcU7NKZflu9So/ZGBJIpINaiDEFcQMixZ8IzduWDfpTYfXRCBPv2cPbZNtNbjULjBz6jOu/awJmF1zjWihfBlaI1+Bm4RlIIuVME4s3fzDSquVK5cbgj/W5zA0YPeuXdKmZQtJliie6pcqlC2tlsG6SW82vCICpyaFtKaN6kvi+LElZuQP9AZhyYf/PWcEmS9La+QrHpsbftPGjdK0oSNmiGfIXKdmdVljLMOdO3ecz8IyPNcvURhEskHPgw2g31x4RQT85NEjhms1llOy2scV5BvSjP4WCQLSkwzbolHHQYRXlzXyhI3m/TSqX0etAmtysQzr1qzxQ4Yd27dL65bNdCEiOxzKq8x7kZ+hARZvDrwiApmVxQsXSL1aNaRF40ayZPEij6cj2zLpG06TLMlL0xr5Crb/bzaWgRoH85cgBJZrrbEM1CAAQwNoAGrdopkkSxhXD4BKFcrp53DvnmNogMWbA69jBCZVEHDiNnhSbHJaou2huIb79DK1Rr6CXgWXZSB4hhAN69SW9evWmnjguWWgAahNqxZKFlSrVT4uL0vVMlg36U2C10R4EegHXrl8mbpCECCSDvh6+Voj3/DUkPQHJSuqVUbQYBk2rPdLhu3btmmVWhuSDGEqlS8ry5d8a5t73iCECBEQtC1ZvFDz87RwcrpyenLjNGoQvLlGoY27xk3a+PNPUrdWTU0HO4aS1ZZ1a9f4cZN+MZawRdPGkti4SOiXqlasoC6ia2iAxeuNYBOBrTVIEqpXrqgp1QRojT7MpZv2da5REGafvmw8fPRQfjBWi4HFaKV4NK5fT77fsP5Z2pTsMA1ALv0Sm3uqVf5YG4DchwZYvJ4IFhGuXbumis3ypUvqzcO8obomoO7Yvq1Km1+11sgXUAdhkToJgaTOUx9J+Q8b/C5X34p+qQn6JYflq1KxvCxftsS6Sa85gkwE2jTZnI8uBxIkSxhf+4K//369brGhsZ+bJSzVEV4E3CTimTo1q0ncmFHVtWvSwFiGdeueFQzphiNmaN64oSQ2QTbWobqxDEtNzHDfukmvLYJEBKTXUyd/pXsLokd8X5tgunTsoCMXyRzNnT1bCoWxyrK3ePDwgRYP69aqrq4eGaVmjRrIj99/r0QBT5881QYgYoakCeKom1SzamUV87k3AFm8PvCZCBcvXtT9CAzZJbhEc8ScI/YmA26EGVOnhjmJhS9g4TlWgOCfCjSnPjEDi9Pv3n3uJm3ZtEmr7VqYM1ZRZd4rV1gyvIbwiQhsyJkwfqySgNOSqit7kplE7RoZz/b8sKg18hXEBViGWtWrSFxz4qdOlkRjgx9+2ODHTdq6dbM0aVhfZybhHvL8lcYykGmyeH3gFREYu37w4G8yZtQIyZ8nl+4tYzEHFWT+3R20baI+DSsy7OCAWasb1q2V2jWqqvWjzkA/NIU4V9qUFOtmtQwO/RKxRZ0a1axleM3gFRHwjadPnayj3+PEiKKTpgf07aOTLfwDGfa0KVOkQJ7crz0RAP0MVJuJAVCtMlWPQHnjzz8/ixkAVXd2QWAVEqNfMs//bjU9D5YMrwO8IgLqUzZo0oqZNWN6GTSgn/YfuApO7kCIN3bMaG3WocIclGWCYQ24SViG6lUqaaEwjXEJsQw//fj878JNImZoVLeOTuAmbqhbs7qsMpbBuklhH14RgS8SLT+roaZ89aXGBJ6wb+9eaWZOTNcyQYgQFrVGvoLpGGvXfKdDAOJGjypJjJv0SYtmxi3aqD8DuJCMxmxsLAPZJlSrSE78NwBZhD14HSxz4uHz3jW+sStYdAdkYeDu4AH9dRl4hHf+V4kQtrVGvoEK9NrvVkv1ShX11E+ZJIFahs2bfvYjtcACorqlKEdcUbtGdVlnSGTJEHbhNRECA0pOVjv16NZVg2jy6gTUr2KuUWiDngVu6mqGDDTtsPGTuaubNv7kfIajGw7LUN9YA4JsVeHWriVrVq2yblIYRbCJgP9M4IisgikQkSO8qzsL0qVKroW2hvVf/lyj0Ab9CGtWr1YyMCmPk59e561bNsuD+44bncMBl7CB6pdiGAsSXSUbuFfuDUAWYQPBIgL6GjIqzRo11B5fBHcM1m1k3CHSpxChfhhszAkJ0KzECU9/ArEAknPmrm7bssWP1AK3EP1SkvixtbmHLBoyb0uGsIUgEwESLFmyWEV2VF7JpnDizZszWz4bPVKKFy742mmNfAU3MylSyBAzygfGCibT+UgI81zAeuAaQgZSz7hJBNPIvCGTRdhAkIhw4cIFmTd3tk6bjmn8ZDJE5NAZs8ji8TkzZ0qRAvneiDrCi4DkYvWqlVK5YnmJFS2S1hE6tm2t81eZigEemRv+x+83SF3zWdDYw+fVtGF9PzJvi1cLn4lATzKV45LGBUJmwfQ4xGeuU5Dm/ZnTpr32EgtfQABMvYCeZuYhpUmWWNq3+UTJQLYNuGTeTM1g6HCyBPH08ODf/rFu0iuHT0Q4Z077CePG6rpWV52A7ZYM03V94aRYw+KAr9DGndu3lQxs+IwR6X1NGHRq30abeVxwyLw3qJiP/Q1sBUXZ+v36dRpcW7w6eEWE+w/uy769e2TYkEG6Ekq1RunTSu+e3XULjTvQGs2YNvWN0Br5CtwcpNjMQWLZOdXlzh3a6543VzzABp8N5saHDKRWE8WNKS2aNFJlq3WTXh28IgJB4eQvP5ecWTLol5c7WxYZ1L+fHD3qQWs0efIbozXyFZz6DjKU0VOfqYDsYYAMrhoC0hQkG7WqVVHLinuJZbBkeHXwiggUiJBWFPgwp3nkklEjhsmpUydVt+8ftG+OHjFCsmVMr67Tm6A18hW4hyuWL9VpgDQu0cLatZOxDDu2O5/hCLJxiWpUrexYqpI8icZapFtdknaLlweviPDk8RPdPcYoR8alH//zT+dP/OKp+T9mhzaqX0+nTruI8CZojXwFK3mXLf1WKpQp/WzGEw1M7GNAkwSQeZNGRdlKkJ04Xixp1aypH5m3xcuB18EyX96DBw8DVJwCfGC61JBnZ0mfRt5/5//pl/8maY18BW7OsiXfSnlDhlhRI+vIzC6dOmhy4aH5LAGfK2Rg7RaFuRTIvJs01kl87jJvi9CF10QIDHyZBM29P+3m1BpFlmgRI7yRWiNfQeGRxv7yZUrpZ5IxbSrp0bWLWk4X7hrCrDdkYDwMuxmoyLdp2Vw2/fzjM+thEboINhGwBLt++UU+7dpZK8lRIrwnGVOnlPSpUryxWiNfQcyw5NvFOvGDlbYsI0GgSCbOdaMjy0DZChk4SJBjtP2khWzZtNG6SS8BwSICX9D27dukU7u2kipJIokbM5qUKFxQGtWtK4Xz5X2jtUa+gswbk/E+KlNST32GHmAZ9u3Z8yy1SgVayVCpgi5mxLVkCDG9IHbwcOgiyES4/+CB9uq69ghQRCI3zqyjMSNHKiHedK2Rr2CCOGQoW6KYrtzKlC619DLu5L69u53PcMQVawwZGBxGkM2AhLbmM+aztm5S6CFIROB0IwCmQ4vpDdENCdiZwL+dPn1KZr9FWiNfQZ2F0fJlShaV6MRRyRNL7x7d5VcTY7kSEQTJNP9DBnoe2P3Wvk1r1XK5KvgWIQufiYCUABlxk4b1VIdPDpxcOKcYX6RqjaZPf+skFr6AzwgylC1ZzMQMyDFSSq8e3TTh4JJakFpl4WHlCh9JbOQYJq5o17qlbDdksDFDyMMnIty5Y8z2qlXSqF5dSQYJokVSd2j9unVqJcDbqjXyFWwhYh1VmeJFJGqEcJI5fRrp06uHIcN+5zMchw6WoVL5cmp1WXLI5s/tWzcbNyngNLZF0OA1EZhwxxKQ+rVraSsmUgv6clFPup9QLq1RWNyhFtbAFO1F33ytzUzot9KkSCJ9e/XU0ZmMlQTEDCuXL1cyxIwaUXs/EPOxwMS2fYYcvCICWQ3MNF8GTes6Nr1BPe3TdWU8XLh185bKMfLlzmmJ4AWoMyz8Zr6ULlbUUWcwblKfnj20OOkKju/du/+MDMQMyDFojYUMNmYIGXhFBGYVjR4xTLNDpPWaNaqv/bkB+apXrlyRoYMGSsY0qfT5YXGHWljDtWtX5Zuv50upooW1DkNlfkDf3nLwt1+dz3C4nCuXLZOKH5VRN4n0a9eOHVS/5Knab+E9vCICwR1pPxrUKZz9/CPCsH+n8gjwuOnZUknrposIb6PWyFf8ff1v1XGVLFJIor4fXts+B/br42eGFDHD8mVLpWK50hpkI8dAv7Rr585/WWYL3+B1jMBJf+SPP+T0qVMBdlSR8sNKdGrXRidYfPDu/ykR3matka9gw7+SwVgGYoZMaVMrGQ4dPPjcTTKfM4tJKpYtpX3SaVIk05H8kMHGDEGH10QAAQ32AhTXiBewGJhslJScWFZr5DuuXr0iX8+bqwXJyOHfk6wZ0unQtMOHn1uGW7duyvKl6JdKKmHohuvetZMqW62bFDT4RISAgLkmc9SqeRNduYT/Si8Cp5lqjYxFsDGCbyAmYzhCsUIFJMr74VS3NXhgf/n998POZzCP9pYsVf1SCf3MmbqHZGPv7t227TMICBYR+DJQTTKehLoCQjG0NLQeFi2Y36E1egsbc0ICNDjNnTNbLQNkoM6AZfjdWAbXqY+LuuRbh34JC0ydoXuXzto7QkuohfcIMhEooK1auVxnGVFhprbQrHEDWbRwgUwY+9lbMdcotMHEkLmzZ+mwBCYIMo186KABJlb73fmM5/qlcqWKq36JbjiHfmmPR1fW4t8IEhEw3RTXGHuOZJixLlSbyWtfunhB5s6aaQtqIQRihrmzZ0rRAvk0tUo8MGzwAD/94tQivl24UMqWLC7RIobXA6hXj+5yYP9+K9TzEj4TQU+gRQt1uBcTGBh/zrAq1JEAd+ltm2sU2mCD6RxzuGjM4KwzMFHkyJE/np36Dv3SQimnZIigSYvePT41ZNhnU6tewCci/H3jhiyYP09VkYnixZaEjCJp2lhn99y/56hw3rx102qNQgFIXGbNmC5FCuSVSOHfleyZ0suIYUPk2LGjzmc49UsL0C8VM4QJpwmLvr17yK8H9ls36QXwmgjUD+YYf5WZPXRZMYKEdCnu0JOnz1N2FIbelB1qYQ2XL1+WWTOn62cbKfw7Wr0fachw/M9jzmc4LPbCb75RyQaFOVLY7LpDv8QaLIuA4RURMK3IhksULaRiOya0dWjTWlN1/sGeZUR3lgihg8uXL+k0kSImBosUzhFAjxw+VI4dPfrs1Hfol76W0sUhQzjJkCaFQ8x34IBNrXqAV0RAUcpGTbqlkieOL507tPPoe/LcLyZNlDw5s2llmdVJlgghiwvnzzusrnE/I4V7R3JkziCjRgyX48efj9lR/ZJWqQtJ5PffUzeJCSOHDv5m3aQA4BURSJWyB6xPz09l+NDBsmvnL86f/Bt0qDHZjeJaisTOuUa2shziuHTposwwZGDgGm5S5nSplQwnThx3PoOY4ZqjSl20oAbZHGQDnJKNJ06Zt4UDXscImFsWjlPo8ZSFuHrlssw2PmzBvLlVawQRrNYo9HDx4gWZPuUrXQCPZchmAujRI41lcIsZ/jYB9DeGDKWKFpEoxjJQZ+iPstVYhsfWTXoGr4nwIlwxgRwzT0nx0a+Ab0p7IaPPrUUIPfz11zmZOplxnA7LkDNLJvls1Eg5dfKE8xnmgLp8RebPmSMlihRSy4D1GNi/rx/90tuOECEC4+K//HyiTsqO9kF4He1CUcdqjV4OLlw4r2TIlzuHkoEha2wtItPnwrWrV2X+3Dla8Xe5SYMG9JU/fv8dNaXzWW8vgk2E06dP686E3LqVP6p+GdUrfSz5DCkggm3MeTnAbaUzUAPo8O9KjiwZZdxno/1YBtzaeYYMGkAbMjB1b8iA/vLH4cNvfWo1WEQgMP5s9CjJkTmTzuBh+jNLyYcOHujQGiVLbNOnLxHnzp7V8f35P8yploHx/RPGjpEz5rBygVrE3Dmz1IWFMOy5GDZ4kBw98u8R/28TgkwEKppUNknLxYjkIAETF/hAZ02frh+0rSO8fGAZJn/xuXFTsykZsmfKoCJIdzKgX5ozCzLkV20ShTnIgGTj0aO30zL4TAREXPiVQwYN0KArTrTIOsmZ5nKySWheIIKVWLw6nDt7Tr76fJIjgA5nLEPWzEoG95gB/RLiSOTyNPdkzZheBg/s99ZaBp+I8PTpE/nd+JMUZrAE8WNGVwUqCy8Q24Hbt2/LjKlTLRFeMbAAn08cL3lzZlMJ94c5ssqkCePk3LmzzmeIHD92TPr06mlihdSa7s6eOYMqCN5GeE2EB+a0379vryoa0yRLIonixNZF48zxd++VpbLsrjWqX6embPz5J+dPLV4miBm+mDTBkMBBBlKrkOOvv/7SnzMlgyXprMSNbOIFYouVy5fpz942eEWER48eyu7du6Rzx/aSNmVyFdy1+6SVjoMXf5k3tEbu6lOIsGXL8wXcFi8XVy5fkWlTJkvxwgV0wSHqVSzD+nVrZdCAfsYlSieJ48dRRfG0qZNV5fo2wisiMF1hwrjPVAdPJoh9YAi4AqowU9YnnZorWxZJnjiBxg/MRaXB/8nTpzqQyj5ezoOWTmI6po+MHTNK9V+IJnGBEO1lSJNSuwsrlCsjs2fOkJMnT6h1D+h3va4PZm/xX+7VwDRWXhHhn3/u6NaXrp066CJBBHeeQBsh5jZpgniSOF5s+TB7VmnWuKEO/RoxbKgMGTjAPl7SgzT26BHDZfiQQfqdQAR2M1BDIKOEO0RjFRXnLh3ay+iRI1SiEdDvel0f/fr0ksHG8q1d851OIvcEr2MEJq1dvHBBbpr/BjQyBLZRXJs4fqzkzJpZ3jfBV/RIEXTCAlkJHtQaXHNTmZiHqaYSTXN6QA9kGvQ+xHVew5gYRh7SgRXQ83nQt8uuBl6HFlK9htd50TXu7808HK/j+b3xcL2O670xGTzQ1zEPPg8ybfH9vM6Lr2Fgmuu98b8Du4aH63V4Pp+D6zr+Tn7GSHr+y/9P47/rf/t/Hf6d9xDQa/DgO+bv5vt8fs0L3pt5bffXod2X1wnoua4Hfy+f1b/em/nuAnq+6/Hu//xHIoZ7R7oYt/68MzYKCF4T4UU4dfKkalzy5szuvGEjOm6OZ284vP4x/G8e/G/HB/yelvz/9TD/HuA1+ocH8Pxn1zg+tFdzjZM4nq4xPwv1a8zD/zU8sATuRHd/8B1Basc1zuu8fp3wz18nlK7hZxyYPl3jfLxjiPDBe/81RGgnf50757xb/40QIcKxo0e0U4qRI/yhuEOtmjXRBvK+vXo4TFTvXlKnZnVtJOELYUobKlU27iDv5tHr0+76IDM1oE9vHV/CUABSta4vMU+OrNLS/O7+5ufu1/C/+bf+xhS2bNrYxCiZ9YPiSyZwZ20rz6NBxXUND8wm6eBG9etoXMNrcEPkzp5FF6G43hvviefzX16DOgpja2iZhPA8KF41bdhAf84gX9drOK7prfNM27RqoTIUbjg+A16nScP60rN7N+nb2+97G9ivrz74ewrkyaViRsiRJUMaaWau4Tn+3xu/A5eo3SctJW+u7GoNYpsTl6b/urVq6PviO+nldg3fDfJs5PPFCubTk5cbDs0S6XHmJeFiuN4XD/4Wvp/2bT4xrlVBHeWDq8UMpgZ1auvf86/3Zl53mHlvrBornC+PJDRuGVYLKU5NE0v2Ns/T78fPe+up0/66deqojUasJ4NI/D3En906d9LP2/U6/h+MxOzZvatmw0jkeEKwiOAorh2WoeZGz5wulabo+APxM/fs3qkyYQLtq1euyJbNm6VHty6apWDbPKk65Bk0ily+dEkfuF4XL1yUa1evqRSAyW19evTQaW9cU8gQh3EmrGdFXvzsmotcc1UVsPyMKmnObJn0y6SohJ+8Z/dufS6jK13X8L5oYGHDJRkUcu3xY8XQNCPFJUaiuN7bJfN8rqMQxXX0AfOlciNDHlKUEH/71q065YP37+d1zHW//bpfJSgsbocIvA432NYtW4zZPq+/W68xnwHvk99Di+W4MaOlqLlB+Qx0ql2XTrJj6xZ9rp/3pn/PNa0Qfz5hvF4DEbKYz5wb9vv16/V9kUnifXGN43Wua5F0+pTJ5mYrotYDHRLE2LB+naZh+b2O92auMb+Dz58DkG7ECuVKa6yhy0w+aSU///ij/j3u7831Oif+/FP7KMqWLCHxzd+DLLy5OVBQJVxy/g3P3pvzddjr/fXcudomHNsciEwDb9W8qawy15w6dUo/J9fr+H9ccP6XNoLAJnoEmQjECYcPHZSB5jTlj+GkQvD15ReT5OSJE35aAvlDkGMw4iVezKh6Qk/+6gv12QKKN8D5C+dlzKjheqolT5RACpoTkcwH1VFP/RCXL11UrQ2/H0vA+yFVSOcWi/oCAu+BjjpuAPYco88ZOxqx2kmPbY188KhtSUWmSJxAScckOkasPLgf8GAtDgSm15Uyr4NPzOswiYImGbIaAYEDgblGlSp8pNYgk7k5sZQM+Xrg4Rpm0NKMwzpbFMDc0JyK+/ft0zW2AeHe3Xt6Ylap+JGSGsvOoUV6nP0MAYHhYlxTv3ZN3dmQOlkS5+vsNb8v4MWH9D8sX7pUqlWqqFYABWybli1kx7atOjExIPAd/LBhg1ozDgKmc7Rv/YnWryjehhSCRASUigfMB4vpQ3JNBqJYwfzKdP9+GCX7EUOHqjo1mjkFsQRoYWCqJ5w+ddKQYKQ5ZbPoyVkgby4ZP3aMEswTkCJ/+fkkPdWjGP+dE5pT8eyZM85n/BtnzpxWEnBD4w6h2ES+7K7L8Q/aJL8yZC+U70O1ODmyZjKuyAC1jJ5AShltTxFzQuPbZk6f2nwmgwOVM3DCzTXXOEY6fiDpUiZXF+YIsmkP4PSEBOVKlVT3JoNxU5hevm/vXucz/g26D5lRVbFsaU1mUPvBlXBffesfuBgrDAlqV6uigXKKRPE1GA0sm8jrrDCvU/XjCsa9cWwMZX3uju3b5amHw5BU7oZ1a6UWr2MOtsTG6mDZthmr6+nACSp8JgJvjpGCfMBMSCAVx5bIOTNnqElzgQ+RhvKhxk3hBsPHz5s7u95EmD9PwAyPHjlMchh/mw+MOEJvTnPTegL9EF9MdFRQIWV+4w5NHD9OCRUQyHCdPXtGrUWBPLk1K0V3F33ZgQVUV4yp/9IQBx+fv4dTnQYXXBFPoNmemURFC+RXtSdxhM4kcptW5x9X6PSbMV1KFyui2Zi0yZOq7+w+1Ms/qOjjPpQy18SJHlV1YKS795sb2hNu3rgpy8zNiWCSYBT//lNjCXAjPZHAMYB4iVSrXFFP6KTGGnRu307rSp7guqaScW2wOIymJP7attVzoRXirF+/VmpWraSxFJaXqSlbjYsdGlO/fSICZgq/vasJXFIbf5DTrUzJYtokzgnmDr5o+pu5aQhu8uR0kMCdLP6hJBg+TANdfFv8b+IIbtqn/kvYThCHfDkJS5BNg2OCaQRmp4z18FRAOWtOfCwBUnFSh1lNUAgJzgRiPSAvZCNo5QZAvjyofz85duyYx5tG55cymKtgAWG0CgVJx/zSwx6vgTjIpCsY10a38BuXg91qWAJPbiQuAi5UmRJFja8eW4uenTu20zjGkxtJbUgXj5Qro2nTNMZN6WpcG75fTzeawxIs1b158YwbybbPjibwxe3y1PbJ71q6ZLFULl9Oi3e4Ufj3O3ZsMy5hwEsR+Xcq37WqV9HsI0oGiMMQudBapOg1EWAo602ZYJE4fmxDgnB6kixetEC/cHeoO2RigpzGbYAs+Yyfj9uC++IJuD1jTFCLC+W6Bktw4vjzZnT/OG/cFGISTuZI4d/TrA9VbXeVpX/QQ/EV/r2JV/gbCN7ZBsS/ewJWgvePdVIXKnMGvaFpaPEEh9R5hsZFEDRT2pQa6BOUeipwckjMmzNb3aFoH0TQm7Nvz55+pmD7B8H+/HlzdMJdDHNypjWnLZYAq+0JEEfdIUMC3DtO2+7GwmMJPBEHi7PSkKBmtcp6QnNTs74qMLeL2hOvw1TEONGi6Ou0btVcB8J5IjU3+rq1a4wlqKwkIDYi0+ZYuh5620S9IgIfDm+kRdNGWjHmBKnycXlZtmSJicafp6RgP30KI4cNVRLg16F+xJ0gWxEQsDL48dQgcmTOqGnI/LlzOm5OD64NH+K5c2dMYPyFtociNcbyjPtsjJzwEEfwOueMZeGGptkd1yarOdVHDR+qFicgPDavg6XTZhfznrgmZ5bMmm715NpghdS/Nyd0cR3e+56mWIeYYNp9+407sA5kSObNcdzQfAYEn2oJ/gjY7eJ1XCNbypQoYq6Jon0FZHoCmjflAnEEQS5uCvl43BTH1p1fArRSfNZYAq6pYdwUrCGp0o7t2ug6XE9g0BhxBOtxcYdYaELam2UynoCEnyyVWgJjDV3EYfeGp4RCSMErInDiU35nKgW+ZDXD8NWrVuof6w5OO0iAj87z8hh35cvPJwQeGBs3ZaRxh3CDcIdyGQKR7iRgDci1wUXCEuBm0Q7K6+TOnlnGGhfquLEenk4aXodr2EbDKZg5XRolgSeyAU7oLyZOVCUtNwD1DOoBkN2Ta0OakJigeKEC6hKSgaEWQHbIUxYK927e7Nnycbmy5gaI9GyILy6Up7+HjZxMHmTwL1KWlEkTOt2UPfLQg2uDJVixzPjqFcrpjcaycyz8TkMCT1koJY5xoerUqKYZPwR6LD/ft2ePx7+Hk3vp4sXmsKyglgPitGjiGA3q6VTn3zesW6duF3UP3CGIs9GQgExYaMMrImDiyHrUrlZVdUOYO1wld9w3fwj+MIExJW0lgbEEdEx5Arldll0UNAFr+P/7H71mjL9xJP6Bb8sYdPx71wgT7c0NJKPEzbRyxXJtQokY7l29OSEsKVJPID3I6VSmRDGJ8N//dd7Q7DQ76HzGv4FFRNOCy8HsUU5b0qpYAte62IBAvwZZG4JpsjYUgl70Ojt37DBuShXtI4A4XcwNTQ3FE/gMuBEb1autrk3ieHE007PbkMCTOwT2mhseBTGk5obuYCzBnkDcLn7Xwd9+k+bmPsElhKTc0Nu2bPF4eACsC6lUV3GytYkJNm3c+FJIALyOEXBf+CBJm5JH9w9unBnTpugsf25sCkf+A2j/IADFtFcoW0oLXyOGDA705gQIp/CjiU9IexKQB0Yc8PjJY/l2EZOiSxiyZdeb80wgcQRQd8CQp3rliipW692zuwlYPfvqQE9CExiSJyeeoIpLwfBFIDDEynKI4KYc8uBCucDNQY9Hw7p11IKSVw+MBICb8IcN66VJw3rq5rVt3Uq2b99m/j1gi+PCDvOcBnVrq3tHuhMSeEpCAFwY3KxPmjdT97hZowayadNG5089g/izTcvm+t64hqLc/RBOkQYGr4nAicJJ5InV/DtzcpZ+u0iWLf020FSfC5jwE8f/lK/nz9Ut9KcNCQL7kIH6+ufOqv9JMMpp68l9cIHfSVEPPxdCHPz1xWMPHTHFWX1f8+fNlaNH/gj0RAO8D9yptd+tklkzpmkg6cl9cAd/z7q138mCb+brTcTnHBh4H8RcK5Yt1VqDZodecA1/L9VtZkxR79lqbjxv/G6qwwxoW/D1fE13eirKucBn8Pff181nsFql3WSh7npwh9xBME5qdPrUyfoe794N/HVCGl4TwRvwIfDhsmb2RTeaOxhnHtCmzsBwz7wOkoQXkcAF3g83GKm5Jy84Bd3BF4Rr6AtY20TWyBsSuMBz7927G6ib4h9Yx8CkxQEBEjGR8EVkcwfXYO18uYZ4hDjGF/Ad8d48VaZDEyFKBAuL1xWWCBYWBpYIFhYGlggWFgaWCBYWBpYIFhYGlggWFiLy/wEaxVZyu4LA5wAAAABJRU5ErkJggg==)
A uniform rod of length
is sliding such that one of its ends is always in contact with a vertical wall and its other end is always in contact with horizontal surface. Just after the rod is released from rest, the magnitude of acceleration of end points of the rod are a and b respectively. The angular acceleration of rod at this instant will be
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)
physics-General