Question

A block of mass $m$ is placed on a smooth inclined plane of inclination $\theta$ and of mass $M$, which inturn is placed on a smooth horizontal surface AB as shown. A horizontal force F is applied on the side of the inclined plane so that the block $m$ is just prevented from slipping over the plane.The value of F is

• A. $mgsin\theta$
• B. $mgtan\theta$
• C. $(M+m)gtan\theta$
• D. $(M-m)gtan\theta$

Answer 1

The correct option is C $(M+m)gtan\theta$

If block is not slipping, that means acceleration of $m$ & $M$ is same.
So, acceleration $=\frac{F_{external}}{(M+m)}$
$acceleration=\frac{F}{(M+m)}$

Using pseudo force:
$\frac{mF}{(m+M)}cos\theta =mgsin\theta$

$\Rightarrow F=g(M+m)tan\theta$