A block of mass m and a pan of equal mass are connected by a string going over a smooth light pulley. 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 be V. , Further, let
`J _(1)=` imulse between particle and pan,
`J _(2)=` impulse imparted to the block and the pan by the string.
Using impulse = change in momentum.
For paticle, `J _(1) = mv - mV….(1),`
For pan,` J _(1) - J _(2) = mV ....(2),`
For block,` J _(2) = m V....(3)`
Solving these three equations, we get `V = (v)/(3)`