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.

A block of mass m and a pan of equal mass are connected by a string go

1.	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.
Answer» Solution :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)`