A spherical ball of mass `M` moving with initial velocity `u` collides elastically with another ball of mass `M`, which is fixed at one end of `L` shaped rigid massless frame as shown in Fig. (a). The `L` shaped frame contains another mass `M` connected at the other end.

The speed of the striking mass after collision is

Options

A. `u//7` backwards
B. `u//3` is same direction
C. `0`
D. `u//2` backwards

Explanation

Let `v_(1)` be the velocity of striking mass after collision & `v_(2)` be the velocity of centre of mass of frame after collision by momentum conservation
`mv=mv_(1)+2mv_(2)`……(`1`)
By angular momentum conservation
`mv(L)/(2)=mv_(1)(L)/(2)+mL^(2)omega`.....(`2`)
`c=1rArrv=(v_(2)+(L)/(2)omega)-v_(1)`.....(`3`)
from (`1`). (`2`) and (`3`)
`omega=(4v)/(7L)`, `v_(1)=-(v)/(7)` & `v_(2)=(4v)/(7)`