Question

A solid sphere rolls without slipping, first horizontally and then up to a point $X$ at height $h$ on an inclined plane before rolling down, as shown. The initial horizontal speed of the sphere is

• A. $\sqrt{10gh/7}$
• B. $\sqrt{7gh/5}$
• C. $\sqrt{5gh/7}$
• D. $\sqrt{2gh}$

Answer 1

The correct option is A $\sqrt{10gh/7}$

$v=\omega R$ , $I=\frac{2m{R}^2}{5}$

by energy conservation

$\frac{I{\omega }^2}{2}+\frac{m{v}^2}{2}=mgh$

on solving we get $v=\sqrt{\frac{10gh}{7}}$