Question

The kinetic energy of a ring of mass $m$ and radius $r$ which rotates about an axis passing through its centre and perpendicular to the plane with angular velocity $\omega$, is :

• A. $mr{\omega }^2$
• B. $m{r}^2{\omega }^2$
• C. $\frac{1}{2}m{r}^2{\omega }^2$
• D. $\frac{1}{2}mr{\omega }^2$

Answer 1

Answer: (C)

$\frac{1}{2}m{r}^2{\omega }^2$

kinetic energy= $\frac{1}{2}m{v}^2$

Now for rotational motion we know,

$v=r\omega$

Substituting the value we get

kinetic energy= $\frac{1}{2}m{\omega }^2{r}^2$