Two wooden blocks of masses M and m are placed on a smooth horizontal surface as shown in figure. If a force P is applied to the system as shown in figure such that the mass m remains stationary with respect to block of mass M, then the magnitude of the force P is

Using the concept of pseudo force in the frame of a block of mass M we have

Then FBD of m is as shown

Let the system accelerate rightwards with the acceleration a
Since m remains at rest w.r.t. M we get from the equation of force as
mgsinβ = macosβ 

⇒a = gtanβ

For the system of (M+m);
P = (M + m)a
= (M + m)gtanβ