Two particles a and b initially at rest


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Two particles A and B initially at rest, move towards each other mutual force of attraction. At the instant when teh speed of A is V and speed of B is 2V, the speed of centre of mass is

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Initially both A and B were at rest. So momentum of centre of mass is 0. And it is given that there is no external force. Hence no change in momentum of centre of mass. And it will remain 0. As momentum(product of mass and velocity) is zero ans mass is not zero, velocity must be 0.

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