As shown, a big box of mass M is resting on a horziontal smooth florr. On the bottom of the box there is a small block of mass m. The block is given an intial speed `v_(0)` relative to the floor, and starts to bounce back and forth between the two walls of the box. Find the final speed of the box when the block has finally come to rest in the box :-

Options

A. 0
B. `v_(0)`
C. `(m)/(M)v_(0)`
D. `(m)/(m + M) v_(0)`

Answer

D

Explanation

`F_(ext) =` zero,
`vec(P) =` constant
`P_(i) = P_(f)`
Finally moving together with velocity v
`mv_(0) = (m + M)v`
`v = (mv_(0))/((m + M))`