Question

Two thin rods each of mass $m$ and length 1 are joined to form L shape as shown. The moment of inertia of rods about an axis passing through free end (O) of a rod end and perpendicular to both the ends is

• A. $\frac{5m{l}^2}{3}$
• B. $\frac{m{l}^2}{6}$
• C. $\frac{5}{7}M{R}^2$
• D. $\frac{7}{12}M{R}^2$

Answer 1

The correct option is A $\frac{5m{l}^2}{3}$

$\begin{array}{c}I=\frac{m{L}^2}{3}+\frac{m{L}^2}{12}M\left(\frac{5l^2}{4}\right)\\ =\frac{m{L}^2}{3}+\frac{m{L}^2}{12}+\frac{5m{l}^2}{4}\\ =\frac{20m{l}^2}{12}\\ =\frac{5m{l}^2}{3}\end{array}$

$\therefore$ Option $A$ is correct .