Question

A quarter disc of radius $R$ and mass $m$ is rotating about the axis $O O'$ (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)

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