A block of mass m and `alpha` 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 speed is V.
Further, let `J_(1)` = impulse between particle and
pan
and `J_(2)` = impulse imparted to the block and the pan by the string
Using, Impulse = change in momentum
For particle `J_(1)=mv-Mv` ….(i)
For pan `J_(1)-J_(2)=mV` ....(ii)
For block `J_(2)=mV` ....(iii)
Solving, these three equation, we get `V=v/3`