A cart of mas M is at rest on a frictionless horizontal surface and a pendulum bob of mass m hangs from the roof of the cart figure. The string breaks, the bob falls on the floor, makes several collision on the floor and finally lands up in a small slot made in the floor. The horizontal distance between the string and the slot is L. Find the displacement of the cart during this process

Explanation

Let the bob falls A the mass of bob -m mass of cart =M
Initially their centre of mass will be at a distance (from P)
`=(mxxL+Mxx0)/(M+m)=m/(M+m)L`
When the bob falls in the slot the CM is at a distance O from P.

shift CM `=0-(mL)/(M+m)`
`=-(mL)/(M+m)` towards left
`=(mL)/(M+m)` towards right.
but there is no exterN/Al force in horizontal direction.
So the cart displaces a distance `(mL)/(M+m)` towards right.