Question

Three identical thin rods each of length l and mass M are joined together to from a letter H. What is the moment of intertia of the system about one of the sides of H

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

Answer 1

The correct option is D $\frac{4M{l}^2}{3}$

The three rods form H, So let $H=I_1\left(AB\right)+I_2\left(EF\right)+I_3\left(CD\right)$

Here we will find about left vertical axis i.e. $I_1$ AB

Moment of inertia of rod AB about the axis is $0$

Moment of inertia of rod CD(parallel axis theorem) about the axis is $M{L}^2$

Moment of inertia of rod EF (perpendicualr axis theorem) about the axis is $\frac{1}{3}M{L}^2$

So, Moment of inertia of the rod about the axis is

$=0+M{L}^2+\frac{1}{3}M{L}^2$

$=\frac{4}{3}M{L}^2$