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

Answer: (C)

$\frac{1}{4}mu^{2}$

Answer 2

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