All surfaces are smooth. The ball of mass `m` is released from `A`. Find the distance travelled by the block of mass `M`.

Explanation

As the external force in the horizontal direction is zero and the system is initially at rest , the horizontal component of c.m. is fixed.
The horizontal distance travelled by the ball towards the right is `(R - r)`.
( When in problems , radius of ball is given , consider it.)
To keep the horizontal component of `c.m.` fixed `(block of mass M + ball m)` has to move towards the left by `x`.
`m(R - r) = (M + m)x`
`x = (m(R - r))/(M + m)`
The horizontal distance travelled by the ball relative to the ground is
`(R - r) - x = (M (R - r))/(M + m)`
If the radius of ball is not given
`mR = (M + m)x rArr x = (mR)/(M + m)`