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. $\frac{3mL}{m+M}$
• B. $\frac{mL}{M+m}$
• C. $\frac{2mL}{M+m}$
• D. $\frac{4mL}{M+m}$

Answer 1

The correct option is B

$\frac{mL}{M+m}$

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