For the system shown in fig, there is no friction anywhere. Masses `m_(1) and m_(2)` can move up or down in the slots cut in mass M. Two non-zero horizontal force `F_(1)` and `F_(2)` are applied as shown. The pulleys are massles and frictionless. Given `m_(1) != m_(2)`

Let `F_(1)` and `F_(2)` are applied in such a way that `m_(1) and m_(2)` do not move w.r.t. M. then what is the magnitude of the acceleration of M? Let `m_(1) gt m_(2)`.

Options

A. `((m_(1)+m_(2))g)/(M+m_(1)+m_(2))`
B. `((m_(1)-m_(2))g)/(M)`
C. `((m_(1)-m_(2))g)/(M+m_(1)+m_(2))`
D. `(F_(1)-F_(2))/(M)`

Answer

C

Explanation

`a=("Net force")/("Net mass") = (F_(1)-F_(2))/(M+m_(1)+m_(2)) = (m_(1)g-m_(2)g)/(M+m_(1)+m_(2))`