Physics - NLM Question with Solution | TestHub

Let $a$ be the horizontal acceleration of the wedge (and thus the block, as it does not slide relative to the wedge).

Consider the forces on the block in the non-inertial frame of the wedge. A pseudo force $ma$ acts horizontally opposite to the wedge's acceleration.

Resolve forces perpendicular to the incline. The normal force $N$ acts outwards from the wedge. The components of gravity ($mg$) and pseudo force ($ma$) acting into the wedge are $mg\cos \theta$ and $ma\sin \theta$ respectively.

For equilibrium perpendicular to the incline: $N=mg\cos \theta +ma\sin \theta$. (Note: $a$ here is the acceleration of the wedge, which would be $F/(M+m)$ if $F$ is the only horizontal force on the system, but the question asks for $N$ in terms of $a$).