A bomb of mass `3m` is kept inside a closed box of mass `3m` and length `4L` at its centre. It explodes in two parts of mass `m` and `2m`. The two parts move in opposite directions and stick to the opposite sides of the walls of box. The box is kept on a smooth horizontal surface. What is the distance moved by the box during this time interval.

Options

A. `0`
B. `L/6`
C. `L/12`
D. `L/3`

Answer

D

Explanation

Let box moves towards right by a distance `x` the displacement of `2m` is `x+2L` and displacemnt of `m` is `x-2L` towards right.

`/_\x_(CM)=(m_(1)/_\x_(1)+m_(2)/_\x_(2)+m_(3)/_\x_(3))/(m_(1)+m_(2)+m_(3))`
`implies 0=3mx+2m(x+2L)+m(x-2l)`
`implies x=-L/3`