Q.
A thin rod of length $L$ and mass $M$ is bent at the middle point $O$ at an angle of $60{^\circ}$. The moment of inertia of the rod about an axis passing through $O$ and perpendicular to the plane of the rod will be
A) $\frac{ML^{2}}{6}$
B) $\frac{ML^{2}}{12}$
C) $\frac{ML^{2}}{24}$
D) $\frac{ML^{2}}{3}$
Explanation
(b) Moment of inertia of a uniform rod about one end$= \frac{ml^{2}}{3}$
$\therefore$ Moment of inertia of the system
$= 2 \times \left( \frac{M}{2} \right)\frac{(L/2)^{2}}{3} = \frac{ML^{2}}{12}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.