Two masses `M_1 and M_2` are connected by a light rod and the system is slipping down a rough incline of angle `theta` with the horizontal. The friction coefficient at both the contacts is `mu`. Find the acceleration of the system, and the force by the rod on one of the blocks.

Explanation

Taking two blocks as system
`(m_(1) + m_(2))g sin theta - (f_(1) + f_(2)) = (m_(1) + m_(2)) a`
`f_(1) = mu N_(1) = mu m_(1) g cos theta , f_(2) = mu N_(2) = mu m_(2) g as theta`
`(m_(1) + m_(2))g sin theta - mu(m_(1) + m_(2))g cos theta = (m_(1) + m_(2)) a`
`a = g sin theta - mu g cos theta`
`m_(1) g sin theta - R - f_(1) = m_(1) a`
`m_(1) (g sin theta - mu g cos theta) - R = m_(1) ( g sin theta - mu g cos theta )`
`R = 0`