A small cubical block is placed on a triangular block M so that they touch each other along a smooth inclined contact plane as shown in fig. The inclined surface makes an angle `theta` with the horizontal. A force F is to be appled on the block m in horizontal direction so that the two bodies move without slipping against each other assuming the floor to be smooth also. determine the
(a) normal force with which m and M press against each other.
(b) magnitude of external force F. Express your answer in terms of m, `M, theta`,and g.

Explanation

When there is no sliding at any contact surface, we may take complete system as a single body.
Considering motion of the system
From FBD of m
`F=(M+m)a` …(i)
`N cos theta = mg` …(ii)
and `F-N sin theta =ma` …(iii)
From eq. (ii)`N=(mg)/(cos theta)`
Solving Eqs, (i), (ii) and (iii) we get
`F=(mg)/(M)(m+M) tan theta`.