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Two blocks A and B of masses m and 2m re...

Two blocks A and B of masses m and 2m respectively are placed on a smooth floor. They are connected by a spring. A third block C of mass m moves with a velocity `v_0` along the line joing A and B and collides elastically with A, as shown in figure. At a certain instant of time `t_0` after collision, it is found that the instantaneous velocities of A and B are the same. Further, at this instant the compression of the spring is found to be `x_0`. Determine (i) the common velocity of A and B at time `t_0`, and (ii) the spring constant.

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Two bodies A and B of masses m and 2 m respectively are placed on a smooth floor. They are connected by a spring. A third body C of mass m moves with velocity v_0 along the line joining A and B and collides elastically with A as shown in Fig. At a certain instant of time t_0 after collision, it is found that the instantaneous velocities of A and B are the same. Further at this instant the compression of the spring is found to be x_0 . Determine (i) the common velocity of A and B at time t_0 , and (ii) the spring constant.

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