Question

A thin rod of length $4l$, mass $4m$ is bent at the points as shown in figure. What is the moment of inertia of the rod about the axis passing point O and perpendicular to the plane of the paper?

• A. $\frac{m{l}^2}{3}$
• B. $\frac{10m{l}^2}{3}$
• C. $\frac{m{l}^2}{12}$
• D. $\frac{m{l}^2}{24}$

Answer 1

The correct option is B $\frac{10m{l}^2}{3}$

Since the mass of rod is 54m and length is 4l.

so massC = m

and length of AB = BO=OC= CD = l

WE, know moment of Inertia of a rod about to end = $\frac{m{l}^2}{3}$

So,moment of Inertia of AB,BO,OC,CD about B,O,O,C respectively = $\frac{m{l}^2}{3}$

FRom parallel axis theorem

Moment of Inertia of AB about O.

$=\frac{m{l}^2}{3}+m{l}^2=\frac{4m{l}^2}{3}$

Similerly od CD about O $=\frac{4m{l}^2}{3}$

SO moment of Inertia Rod about O

$=\frac{m{l}^2}{3}+\frac{m{l}^2}{3}+\frac{4m{l}^2}{3}+\frac{4m{l}^2}{3}$

$=\frac{10m{l}^2}{3}$

Hence option(B) is correct.