A block of mass m and a pan of equal mass are connected by a string going over a smooth light pulley as shown in figure. Initially the system is at rest when a particle of mass m falls on the pan and sticks to it. If the particle strikes the pan with a speed v find the speed with which the system moves just after the collision.

Explanation

Let the required sped be `V`. Further let `J_(1)` be the impulse between the particle and the pan and `J_(2)` be the impulse imparted to the block and the pan by the string. Using impulse as the change in momentum we have the following equation.
For particle `J_(1)=mv-mV`........i
For pan `J_(1)-J_(2)=mV` ...........ii
For block `J_(2)=mV`..........iii
Solving eqn i - iii we get `V=v//3`