In the figure shown, all surfaces are smooth and the pulley is massless. A constant force of magnitude `F = (mg)/(2)` is acting on the block of mass M. The acceleration of the block M is :

Options

A. `(mg)/(2(m + M))` towards right
B. `(mg)/(2(m - M))` towards rights
C. `(mg)/(2(m - M))` towards left
D. `(mg)/(2(m + m))` toward left

Answer

D

Explanation

mg - T = ma …(i) and T - F = Ma ….(ii)
Adding equation (i) and equation (ii)
`mg - F = ma + Ma mg - (mg)/(2) = a (M + m)`, `a = (mg)/(2)(M + m)` (Towards left)