Question

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 then a particle of mass $m$ falls on the pan and sticks to it. If the particle strikes the pan with a speed $\nu$, and the speed with which the system moves just after the collision is $\frac{\nu }{n}$. Then n is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

For particle, $J_1=m{v}^{\prime }-mv$ ................(1)

$v^{\prime }-$ initial velocity

for pan; $J_1-J_2=mv$ ................(2)

for pan; $J_2=mv$ . ...............(3)

By solving $\Rightarrow v=\frac{v^{\prime }}{3}$