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 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 out the force constant of the spring.
Answer» Solution :According to the principle of conservation of ENERGY, `1/2mc_(0^2)=1/2mv^2+1/2times2mv^2+1/2kx_(0^2)` or,`mv_(0^2)=3mv^2+kx_(0^2)` [k=force constant of the spring] or, `mv_(0^2)=3M(v_0/3)^2+kx_(0^2)or,k=2/3(mv_(0^2))/x_(0^2)`