Question

A circular ring of mass $ m $ and radius $ r $ is rolling on a smooth horizontal surface with speed $ u $ . Its kinetic energy is :

• A. $ \frac{1}{8}mu^{2}$
• B. $ \frac{1}{4}mu^{2}$
• C. $ \frac{1}{4}mu^{2}$
• D. $ mu^{2}$

Answer 1

The Correct Option is C

$K.E.$ of rotation $=\frac{1}{2} I \omega^{2}=\frac{1}{2} \frac{m r^{2}}{2} \times \omega^{2}$ $=\frac{1}{4} m r^{2} \times \frac{v^{2}}{r^{2}}$ $=\frac{1}{4} m u^{2}$