A block speed 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, then a particle of mass `m` falls on the pan ad 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`.
As there is sudden change in the speed of the block, the tension must change by a large amount during the collision.

Let `N` = magnitude of the contact force between the particle and the pan
`T`=tension in the string
Consider the impulse imparted to the particle. The force is `N` is in upward direction and the impulse is `intN` dt. This should be equal to the change in its momentum.
Thus, `intN" "dt=m u-mV`. ....(i)
Similarly considering the impulse imparted to the pan,
`int(n-T)dt=mV`....(ii)
and that to the block, `intTdt=mV` .....(iii)
Adding(ii)and(iii),
`intN dt=2mV`
comparing with (i)
`m u-mV=2mV` or `V=u//3`.