A wedge of mass `m_2` is kept on a spring balance. A small block of mass `m_1` can move along the frictionless incline of the wedge. What is the reading of the balance while the block slides? Ignore the recoil of the wedge.

Explanation

We consider wedge and block as our system. friction reaction force between block and wedge is internal force. `N_(x) and N_(y)` represent reactions on the wedge by the balance.
From Newton's second law, for system block and wedge.
`N_(Y)-(m_(1)g+m_(2)g)=(m_(1)+m_(2))(a_(CM))_y` ...................i
`(a_(CM))_(y)=(m_(1)a_(1y)+m_(2)a_(2y))/(m_(1)+m_(2))=(m_(1)(-gsin^(2)theta)+0)/(m_(1)+m_(2))`.............ii
Note that the block has acceleration of magnitude `g sin theta` along an incline `y`-component of this acceleration is `gsin^(2)theta`. from eqn i and iii
`N_(Y)=(m_(1)g+m_(2))g+(m_(1)+m_(2))(a_(CM))_(y)`
`=(m_(1)+m_(2))g+(m_(1)+m_(2))((-m_(1)gsin^(2)theta)/(m_(1)+m_(2)))`
`=(m_(1)+m_(2))g-m_(1)gsin^(2)theta)`