Q. What is the moment of inertia of solid sphere of density $\rho$ and radius $R$ about its diameter?
A) $\frac{105}{176}R^{5}\rho$
B) $\frac{105}{176}R^{2}\rho$
C) $\frac{176}{105}R^{5}\rho$
D) $\frac{176}{105}R^{2}\rho$
Explanation
(c) $I = \frac{2}{5}MR^{2} = \frac{2}{5}\left( \frac{4}{3}\pi R^{3}\rho \right)R^{2} = \frac{8}{15} \times \frac{22}{7}R^{5}\rho$
$I = \frac{176}{105}R^{5}\rho$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.