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. The maximum height (in $m$) attained by the combined mass is

Answer 1

$2mv=(2m+2m)v^{\prime }$

$v^{\prime }=\frac{v}{2}=\sqrt{\frac{gL}{2}}<\sqrt{2gL}$


$0=v^{{}^{\prime }2}-2gh$

$\frac{gL}{2}=2gh$

$h=\frac{L}{4}=\frac{5}{4}$

$=1.25m$