Q. A uniform rod of length ‘$2L$’ has mass per unit length ‘$m$’. The moment of inertia of the rod about an axis passing through its centre and perpendicular to its length is
A) $\frac{2}{3}mL^{2}$
B) $\frac{1}{3}mL^{2}$
C) $\frac{2}{3}mL^{3}$
D) $\frac{4}{3}mL^{3}$
Explanation
(c) $I = \frac{ML^{2}}{12} = \frac{(m \times 2L) \times (2L)^{2}}{12} = \frac{m \times 2L \times 4L^{2}}{12} = \frac{2mL^{3}}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.