A triangular block of mass M rests on a smooth surface as shown in figure. A cubical block of mass m

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A triangular block of mass M rests on a smooth surface as shown in figure. A cubical block of mass m rests on the inclined surface. If all surfaces are frictionless, the force that must be applied to M so as to keep m stationary relative to M is :

Accepted Answer

F.B.D. of wedge is w.r.t. ground and
F.B.D. of block is w.r.t. wedge.
Let a is the acceleration of wedge due to force F.
F_P is pseudo force on block
mg sin 30^o − ma cos 30^o = 0     [Equilibrium of block in x direction w.r.t. wedge]
a = g tan 30^o
F = ( M + m)a             [Newtons II law for the system of block and wedge in horizontal direction]
⇒    F = (M + m) g tan 30^o

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