A rod of mass m is supported on a wedge of mass M shown in fig. Find the accelerations of rod and wedge in the arrangement. The friction between all contact surfaces in negligible.

Explanation

Compose of acceleration of M and m perpendicular to the incline should be same as both always remain in contact.

For this `a_(2)=a_(1) sin theta` …(i)
For M: `N sin theta-N=Ma_(1)` …(ii)
For m: `mg cos theta-N=ma_(2)` ...(iii)
Solving equation (i), (ii) and (iii), we get
`a_(1)=(mg sin theta)/(M+m sin^(2)theta), a_(2)=(mg sin^(2) theta)/(M+m sin^(2)theta)`.