A large cubical shaped block of mass `M` rests on a fixed horizontal surface. Two blocks of mass `m_(1)` and `m_(2)` are connected by a light inextensible string passing over a light pulley as shown. Neglect friction everywhere. Then the constant horizontal force of magnitude `F` that should be applied to `M` so that `m_(1)` and `m_(2)` do not mov relative to`M` is:

Options

A. `F=m_(2)/(m_(1))(m_(1)+m_(2)+M)g`
B. `F=m_(1)/(m_(2))(m_(1)+m_(2)+M)g`
C. `F=m_(1)/(m_(2))(m_(1)+M)g`
D. `F=m_(2)/(m_(1))(m_(1)+M)g`

Answer

B

Explanation

Let a be the acceleration of cubical block of mass `M` from gorund frame. Them from the frame of block of mass `M` , force on `m_(1)` and `m_(2)` are as shown. Hence for `m_(1)` and `m_(2)` to remain at rest in frame of `M`
`m_(2)a=m_(1)g` or `a=m_(1)/(m_(2))g`
:. `Fm_(1)/m_(1)(m_(1)+m_(2)+M)g` .