A bar of mass `m_(1)` is placed on a plank of mass `m_(2)` which rests on a smooth horizontal plane . The coefficient of friction between the surfaces of bar and plank is k . The plank is subjected to a horizontal force F depending on time t as F = at , where a is a constant . The moment of time `t_(0)` at which the plank starts sliding is :

Options

A. `(a kg )/(m_(1) + m_(2))`
B. `((m_(1) + m_(2)) kg)/(a)`
C. `((m_(1) + m_(2)) g)/(ka)`
D. `(ka)/((m_(1) + m_(2))g)`

Answer

B

Explanation

The plank will start sliding if applied force = frictional force
` a t_(0) = k( m_(1) + m_(2))g`
`t_(0) = ((m_(1) + m_(2)) kg)/(a)`