A particle of mass m is placed at rest on the top of a smooth wedge of mass M, which in turn is placed at rest on a smooth horizontal surface as shown in figure. Then the distance moved by the wedge as the particle reaches the foot of the wedge is :

Explanation

There is no external force in horizontal direction on the wedge block system, So the x-coordinate of the C.O.M of the wedge block system is at rest

Let us assume that wedge move x when block reaches the ground. We can use the following relation when
x - coordinate of C.O.M is at rest
`m_(1)x_(1)=m_(2)x_(2)`
`Mx=m(l-x)`
`x=(ml)/(m+M)`