Question

Two identical thin uniform rods of each mass $m$ and length $l$ are joined to form $L$ shape. Find the moment of inertia of this system about an axis passing through the point at which both rods are joined and perpendicular to their lengths.

• A. $\frac{1}{12}m{l}^2$
• B. $\frac{4}{3}m{l}^2$
• C. $\frac{1}{3}m{l}^2$
• D. $\frac{2m{l}^2}{3}$

Answer 1

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

Given mass and length of each rod is $m$ and $l$ respectively.

For the given axis of rotation, each rod will be rotating about an axis passing through one of its ends and perpendicular to its length.
$I_1=I_2=\frac{m{l}^2}{3}$
So, M.I. of the system is,
$I=I_1+I_2=\frac{m{l}^2}{3}+\frac{m{l}^2}{3}$
$\therefore I=\frac{2m{l}^2}{3}$

Hence, $\left(D\right)$ is the correct answer.