Question

A solid sphere of mass $M$ and radius $R$ is hit by a cue at a height $h$ above the centre $C$. If the value of $h$ for which the sphere will roll without slipping is $\frac{x}{5}R$. Find $x$

Answer 1

Let $J=$ linear impulse
For rolling without sliding
$v=R\omega =R=\left(\frac{Angularimpulse}{I}\right)$
$\therefore \left(\frac{J}{M}\right)=R\left(\frac{Jh}{\frac{2}{5}M{R}^2}\right)$
$\therefore h=\frac{2}{5}R$