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In figure E and Vcm represent the total energy and speed of centre of mass of an object of mass 1 kg in pure rolling. The object is:

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Important Questions on Centre of Mass, Momentum and Collisions

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Two particles which are initially at rest move towards each other under the action of their mutual attraction. If their speeds are v and 2v at any instant, then the speed of center of mass of the system is,
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Two particles of masses m1 and m2 have equal kinetic energies. The ratio of their momentum is:
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A ball hits the floor and rebounds after an inelastic collision. In this case
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During inelastic collision between two objects, which of the following quantity always remains conserved?
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A 1 kg ball moving at 12 m s-1 collides with a 2 kg ball moving in opposite direction at 24 m s-1. If the coefficient of restitution is 23, the their velocities after the collision are