Question

what horizontal force f be given to the wedge of mass M so that a block of mass m placed on it remains stationary with respect to the wedge. the magnitude of the force is

• A. Mg cot $\theta$
• B. $(M+m)gsec\theta$
• C. $(M+m)gtan\theta$
• D. $(M+m)gcosec\theta$

Answer 1

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

$a=\frac{F}{m+M}⟶\left(1\right)$

The block will experience a force of $ma$ and an equal opposite force will be exerted on the wedge.

Now, Since the block does not slide down

$Ma\cos \theta =Mgsina$

$a=g\tan \theta ⟶\left(2\right)$

Substituting in $\left(1\right)$

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