A block of mass` m` is placed on another block of mass `M` which itself is lying on a horizontal surface .The coefficient of friction between two blocks is `mu_(1) `and that between the block of mass `M` and horizontal surfece is `mu_(2)` What maximum horizontal force can be applied to the lower block move without separation?

Options

A. `(M +m) (mu_(2) - mu_(1))g`
B. `(M - m) (mu_(2) - mu_(1))g`
C. `(M - m) (mu_(2) + mu_(1))g`
D. `(M +m) (mu_(2) + mu_(1))g`

Answer

d

Explanation

Here the force applied should be such that friction force acting on the upper block of `m` should not be more than the limiting friction`(= mu_(1) mg)` let the system moves with acceleration a Then for whole system
`F - mu_(2)(M + m)g = (M + m)a`...(i)
For block of m.
`f_(1) = ma or mu_(1) mg = ma or a = mu_(1)g`...(ii)
From Eqs (i) and (ii) we get
`F = (M +m)g(mu_(1) + mu_(2))`