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A big ball of mass M, moving with velocity u strikes a small ball of mass m, which is at rest. Finally, a small ball attains velocity u and a big ball v. What is the value of v:-

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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 A and B approach each other at right angles. Skater A has a mass 30 kg and velocity 1 m s-1 and skater B has a mass 20 kg and velocity 2 m s-1. They meet and cling together. Their final velocity of the couple is:
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Two bodies of mass 1 kg and 3 kg have position vectors i^+2j^+k^ and -3i^-2j^+k^, respectively. The centre of mass of this system has a position vecotor:
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A ball moving with velocity 2 m s-1 collides head-on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m s-1 ) 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 v and 2v at any instant, then the speed of centre of mass of system will be
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A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of 2 m s-1. When the stone reaches the floor, the distance of the man above the floor will be.
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Two persons of masses 55 kg and 65 kg, respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water, then the centre of mass of the system shifts by