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A body has its centre of mass at the origin. The xcoordinates of the particles

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Important Questions on Centre of Mass, Linear Momentum, Collision

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In which of the following cases, the centre of the mass of a rod is certainly not at its centre.
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If the external forces acting on a system have zero resultant, the centre of mass
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A non-zero external force acts on a system of particles. The velocity and the acceleration of the centre of mass are found to be v0 and a0 at an instant t. It is possible that
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Two balls are thrown simultaneously in the air. The acceleration of the centre of mass of the two balls while in air
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A block moving in air breaks in two parts and the parts separate, then 
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A ball hits a floor and rebounds after an inelastic collision. In this case
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A body moving towards a finite body at rest collides with it. It is possible that