Question

A uniform circular ring of mass $400\text{g}$ and radius $10\text{cm}$ is rotated about one of its diameter with angular speed of $30\text{rad/s}$. The kinetic energy of the ring is -

• A. $0.9\text{J}$
• B. $0.7\text{J}$
• C. $0.5\text{J}$
• D. $0.3\text{J}$

Answer 1

The correct option is A $0.9\text{J}$

Given:
Radius, $r=10\text{cm}=0.1\text{m}$
Mass, $m=400\text{g}=0.4\text{kg}$
Angular speed, $\omega =30\text{rad/s}$

The moment of inertia $I$ of the circular ring about its diameter is,

$I=\frac{1}{2}m{r}^2=\frac{1}{2}\left(0.4\right)(0.1{)}^2=2\times {10}^{-3}{\text{kg-m}}^2$

The kinetic energy is,

$KE=\frac{1}{2}I{\omega }^2=\frac{1}{2}\times 2\times {10}^{-3}\times {30}^2=0.9\text{J}$

Hence, option $\left(A\right)$ is the correct answer.