In fig. mass `m` is being pulled on the incline of a wedge of mass M. All the surfaces are smooth. Find the acceleration of the wedge.

Explanation

Constraint relation

It is clear from above discussion
`a_(x)=A(1-cos theta)`
and `a_(y)=A sin theta`
Equations of motion
Considering the motion of wedge in horizontal direction
For wedge
`T=T cos theta+N sin theta=MA`
Considering the motion of block parallel and perpendicular to the sloping side in horizontal direction
For block: In the direction parallel to inclined surface,
`mg sin theta-T=ma_(x)=MA(1-cos theta)`
or `T=mg sin theta =MA(1-cos theta)` ...(ii) In the direction perpendicular to inclined plane,
`mg cos theta-N=ma_(y) =mA sin theta`
`N=mg cos theta =mA sin theta` ...(iii)
Substituting the value of N from (ii) and (iii) in (i) we get,
`A=(mg sin theta)/(M+2m(1-cos theta))`.