A block of mass $m$ is on a wedge of mass $M$. Wedge $M$ moves towards left with an acceleration $a_0$ . If all surfaces are smooth, then find the acceleration of the block with respect to the wedge.

If $a$ is the acceleration of the block down the plane with respect to the wedge, then acceleration of the block with respect to the ground will be $=(a\cos \theta - a_0)$ towards right. Let $N$ be the force of interaction between block and the wedge.

For the motion of the wedge

                               $N \sin \theta = M{a}_0$                   …(i)

For the motion of the block

                              $N \sin \theta = m(a\cos \theta -a_0)$   …(ii)

After solving equations (i) and (ii), we get

                                 $a=\left[\frac{(M+m)a_0}{m\cos \theta }\right]$ .