Question

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

Answer 1

Let the bob falls at 'A' the mass of bob=m

mass of cart=M

Initially their centres of mass will be at a distance (from P)

$=\frac{m\times L+M\times 0}{M+m}=\frac{m}{M+m}L$

When,the bob falls in the slot the CM is at a distance 'O' from P.

Shift in CM=$0-\frac{mL}{M+m}$

=$-\frac{mL}{M+m}$ towards left

=$\frac{mL}{M+m}$ towards right

But there is no external force in horizontal direction.

So the cart displaces a distance $\frac{mL}{M+m}$ towards right.