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A big ball of mass , moving with velocity strikes a small ball of mass , which is at rest. Finally, a small ball attains velocity and a big ball . What is the value of :-
(a)
(b)
(c)
(d)

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Important Questions on Centre of Mass, Momentum and Collisions
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A particle of mass m moving with speed v towards east strikes another particle of same mass moving with same speed v towards north. After striking, the two particles fuse together. With what speed this new particle of mass 2 m will move in north-east direction?

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Two ice skaters and approach each other at right angles. Skater has a mass and velocity and skater has a mass and velocity . They meet and cling together. Their final velocity of the couple is:

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For inelastic collision between two spherical rigid bodies

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Two bodies of mass and have position vectors and , respectively. The centre of mass of this system has a position vecotor:

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A ball moving with velocity collides head-on with another stationary ball of double the mass. If the coefficient of restitution is , then their velocities (in ) after collision will be

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Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are and at any instant, then the speed of centre of mass of system will be

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A man of mass is standing in a gravity free space at a height of above the floor. He throws a stone of mass downwards with a speed of . When the stone reaches the floor, the distance of the man above the floor will be.

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Two persons of masses and , respectively, are at the opposite ends of a boat. The length of the boat is and weighs . The man walks up to the man and sits with him. If the boat is in still water, then the centre of mass of the system shifts by
