Question

A quarter disc of radius $R$ and mass $m$ is rotating about the axis $O{O}^{\prime }$ (perpendicular to the plane of the disc) as shown. Rotational kinetic energy of the quarter disc is

• A. $\frac{1}{2}m{R}^2{\omega }^2$
• B. $\frac{1}{4}m{R}^2{\omega }^2$
• C. $\frac{1}{8}m{R}^2{\omega }^2$
• D. $\frac{1}{16}m{R}^2{\omega }^2$

Answer 1

Answer: (B)

$k=\frac{1}{2}I{\omega }^2$
$=\frac{1}{2}\left(\frac{m{r}^2}{2}\right){\omega }^2$
$k=\frac{1}{4}m{r}^2{\omega }^2$