Question

A cart of mass M is at rest on a frictionless horizontal surface and a pendulum bob of mass m hangs from the roof of the art. The string breaks, the bob falls on the floor, makes several collisions 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 the process ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

The net external force on the cart + pendulum system in horizontal direction is zero.
$\therefore$ $△$ $x_{cm}$ = 0, let us take right as postive, the pendulum moves towards right, so the cart should move left.
$\therefore$$△$ $x_{cm}$ = $\frac{m△x_{bob}-M△x_{cart}}{m+M}$ = 0
Now, the bob moves L towards right with respect to cart.
$\therefore$ L = $△$$x_{bob}$ + $△$$x_{cart}$
$\Rightarrow$ m(L - $△$$x_{cart}$) - M $△$$x_{cart}$ = 0
$\Rightarrow$$△$$x_{cart}$ =$\frac{mL}{m+M}$