Question

A uniform rod of length 2L has a mass per unit length m'. The moment of inertia of the rod about an axis passing through its center and perpendicular to its length is

• A. $\frac{2}{3}m{L}^2$
• B. $\frac{1}{3}m{L}^2$
• C. $\frac{2}{3}m{L}^3$
• D. $\frac{4}{3}m{L}^3$

Answer 1

The correct option is B $\frac{1}{3}m{L}^2$

$\begin{array}{c}\text{Moment of inertia of rod about axis passing}\\ \text{through its center and perpendicular to}\\ \text{it's length}=\frac{m{l}^2}{12}\\ \frac{m\times 4L^2}{12}=\frac{m{L}^2}{3}\\ \text{Hence option}B\text{is corvect}\end{array}$