Q. A metal sphere of radius $r$ and specific heat $c$ is rotated about an axis passing through its centre at a speed of $n$ rotations per second. It is suddenly stopped and 50% of its energy is used in increasing its temperature. Then the rise in temperature of the sphere is
A) $\frac{2}{5}\ \frac{\pi^{2}n^{2}r^{2}}{c}$
B) $\frac{1}{10}\ \frac{\pi^{2}n^{2}}{r^{2}c}$
C) $\frac{7}{8}\pi r^{2}n^{2}c$
D) $5\left\lbrack \ \frac{\pi rn}{14c}\ \right\rbrack^{- 2}$
Explanation
(a) Here, $\frac{50}{100}\ (KE$ of rotation) = $c\ m\ \theta$
$\frac{1}{2}\left( \frac{1}{2}I\omega^{2} \right) = cm\theta\frac{1}{4}(\frac{2}{5}Ir^{2}\ )(2\pi n\ )^{2} = cm\theta$
$\theta = \frac{2}{5}\frac{\pi^{2}n^{2}r^{2}}{c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.