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 cart. The string breaks, the bob falls on the floor, makes several collisions on the floor and finally lands up in a small slot made on the floor. The horizontal distance between the string and the slot is 'L'. Find the displacement of the cart during this process.

• A. $\frac{ml}{M+m}$ to the right
• B. $\frac{ml}{M+m}$ to the left
• C. $\frac{Ml}{M+m}$ to the right
• D. $\frac{Ml}{M+m}$ to the left

Answer 1

The correct option is B $\frac{ml}{M+m}$ to the left

Let displacement of the cart be $x_c=-x$


Displacement of the bob is



$x_b=(L-x)$
$(x_{CM}{)}_{system}=0$
$M_{cart}{x}_{cart}+M_{bob}{x}_{bob}=0$
$x=\frac{mL}{m+M}$