Question

A square frame $ABCD$ is formed by four identical rods each of mass 'm' and length 'l' This frame is in $XY$ -plane such that side $AB$ coincides with $X$-axis and side $AD$ along $Y$-axis. The moment of inertia of the frame about $X$-axis is

• A. $\frac{5 ml^2}{3}$
• B. $\frac{2 ml^2}{3}$
• C. $\frac{4 ml^2}{3}$
• D. $\frac{ml^2}{12}$

Answer 1

The Correct Option is A

In the given figure,
$I=I_{A B}+I_{B C}+I_{C D}+I_{D A}=0+\frac{m l^{2}}{3}+m l^{2}+\frac{m l^{2}}{3}$

or $\,\,\,\,\, I=\frac{5 ml^{2}}{3}$