^Block at rest w.r.t . accelerating wedge

^Block at rest w.r.t . accelerating wedge

Let complete system has acceleration a  w.r.t. ground

but the block (mass, m) is to

be kept at rest relative to wedge                                                     

NSL for block + wedge is,

(M + m) a = F

To keep m at rest relative to wedge

ma cosθ = mg sinθ  or a = gtanθ

Thus the minimum horizontal force needed should

Be, F = (M + m) g tanθ

Also the normal pressing force exerted by wedge on block is, N = mgcosθ + masinθ = mg secθ