Question

A block of mass $2m$ is attached to a string of length $L=5m$. The block is released when the string is horizontal, it picks up a particle of $2m$ kept at rest at the lowest point. if the horizontal surface is rough with friction coefficient $0.5$ and collision is elastic, head-on, the distance (in $m$) travelled by the block on the rough surface

Answer 1

After the head-on collision, velocities will be exchanged.

$0=v^2-2\mu gd$
$0=2gL-2\mu gd$

$d=\frac{L}{\mu }=\frac{5}{\frac{1}{2}}=10m$