In Fig. a pulley is shown which is frictionless and a ring of mass `m` can slide on the string without any friction. One end of the string is attached to point `B` and to the other end, a block `'P'` of mass `m` is attached. The whole system lies in vertical plane.
If block `'C'` mentioned above was released from some height and collided with `'P'` with some velocity `u`, then find the velocity of the ring just after the collision. The collision is perfectly inelastic.

Options

A. `u`
B. `u/2`
C. `u/4`
D. `u/3`

Answer

D

Explanation

From constraints, we have initially
`v_(2)=2v_(1)sinthetaimpliesv_(2)=v_(1)`
Let `I` be the impulse generated in the string

`I=-2mv_(2)-(-"mu")impliesmv_(1)+2mv_(2)="mu"`
`impliesv_(1)+2v_(1)=uimpliesu_(1)=u/3`