A block is placed on a smooth wedge of inclination angle $ heta$ with the horizontal. What minimum

Question

A block is placed on a smooth wedge of inclination angle $	heta$ with the horizontal. What minimum acceleration should be given to the wedge in the horizontal direction so that the block starts moving up along the incline?

Professor PC Thomas Classes · Answer

In the non-inertial reference frame of the accelerating wedge, a pseudo force $ma$ acts on the block horizontally in the direction opposite to the wedge's acceleration. For the block to move up the smooth incline, the component of the pseudo force directed up the incline must overcome the component of gravity directed down the incline. Therefore, $ma \cos 	heta > mg \sin 	heta \implies a > g 	an 	heta$.