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A rigid body of mass m rotates with angular velocity ω about an axis at a distance d from the centre of mass G. The radius of gyration about a parallel axis through G is K. The kinetic energy of rotation of the body is :-

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Important Questions on Rotational Mechanics

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JEE Main/Advance
IMPORTANT
A weightless horizontal rod is acted on by upward parallel forces of 2 N and 4 N at ends A and B respectively. The total length of the rod AB=3 m. To keep the rod in equilibrium, a force of 6 N should act in the following manner.
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A rod is hinged at its centre and rotated by applying a constant torque starting from rest. The power developed by the external torque as a function of time is :-
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JEE Main/Advance
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If a ring, a disc, a solid sphere and a cylinder of same radius rolls down on inclined plane, the first one to reach the bottom will be :-
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JEE Main/Advance
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A body is rolling without slipping on a horizontal surface and its rotational kinetic energy is equal to its translational kinetic energy. The body is a 
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A cubic block of mass m and side length b is placed on a smooth floor. A smooth and rigid rod of length L and with negligible mass is leaning against the block. A sphere of mass M is attached to the upper end of the rod. The lower end of the rod is fixed at point-O, but the rod can rotate freely around the point within the vertical plane. Initially the angle between the rod and the floor is α while the system is at rest. After releasing, find the speed of the block when the angle between the rod and the floor is β

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A disc of mass M and radius R rolls on a rough horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is v, the height to which the disc will rise will be :-

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IMPORTANT

A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity v ms-1. If it is to climb the inclined surface then v should be:-

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JEE Main/Advance
IMPORTANT

A rod hinged at one end is released from the horizontal position as shown. in the figure. When it becomes vertical its lower half separ tes without, exerting any reaction at the breaking point. Then the maximum angle 'θ' made by the hinged upper half with the vertical is

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