The bodies A and B of masses m and 2m respectively are put on a smooth floor. They are connected by a spring . A third body C of mass m moves with a velocity `v_0` along the line joining A and B and collides elastically with A as shown in fig1.18.At a certain instant of time `t_0` after the 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`. FInd out the common velocity of A and B at time `t_0` and (ii) the force constant of the spring.

Explanation

After elastic collision, C will same to rest and A will gain in velocity `v_0` (as their mass are the same).

Let us assume that the common velocity of A and B is v, at time `t_0` after the collision.
According to the principle of conservation of momentum,
`mv_0=mv+2mv or,v=v_0/3`