Question

Two blocks A and B of masses m and 2m respectively placed on a smooth floor 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. At a certain instant of time after collision it is found that the instantaneous velocities of A and B are same then :

• A. the common velocity of A and B at time t${}_0$ is v/3.
• B. the spring constant is k $=\frac{3m{v}_0^2}{2x_0^2}$.
• C. the spring constant is k $=\frac{2m{v}_0^2}{3x_0^2}$.
• D. none of these

Answer 1

The correct option is A the common velocity of A and B at time t${}_0$ is v/3.

Since the masses of A and C are same and the collision is elastic, their velocities are exchanged after the collision. So, now the system is (A+B) and initially B is at rest wheras, A has velocity $v_0$. After some time they have same velocities, so conserving momentum
${mv}_0=(m+2m)v$

$v=\frac{v_0}{3}$