A wooden wedge of mass M and inclination angle $\alpha$ rest on a smooth floor. A block of mass m is kept on wedge. A force F is applied on the wedge as shown in the figure, such that block remains stationary with respect to wedge. The magnitude of force F is                          [AIIMS 2018]

Since, F = (M + m)a                   ……. (i)

Normal, $N = (mg \cos \alpha + ma \sin \alpha )$

So, we apply pseudo force on the block by observing it from the wedge.

Now, from free body diagram of block, we get

$ma \cos \alpha = mg \sin \alpha$

$\Rightarrow a = g\frac{\sin \alpha }{\cos \alpha } \Rightarrow a = g \tan \alpha .......\left(\mathrm{ii}\right)$

Now, from Eqs. (i) and (ii), we get

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