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 outthe common velocity of A and B at time t_0and (ii) the force constant of the spring.

The bodies A and B of masses m and 2m respectively are put on a smooth

1.	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 outthe common velocity of A and B at time t_0and (ii) the force constant of the spring.
Answer» Solution :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`