Question

A uniform thin rod of length $L$ and mass $M$ is bent at the middle point $O$ as shown in figure. Consider an axis passing through its middle point $O$ and perpendicular to the plane of the bent rod. Then moment of inertia about this axis is :

• A. $\frac{2}{3}m{L}^2$
• B. $\frac{1}{3}m{L}^2$
• C. $\frac{1}{12}m{L}^2$
• D. dependent on $\theta$

Answer 1

The correct option is C $\frac{1}{12}m{L}^2$



Moment of inertia of rod about O is sum of moment of inertia of both halfs.

$I_0=I_1+I_2$
using moment of inertia of rod about corner, we get
$I_0=\frac{\left(m/2\right){\left(\frac{L}{2}\right)}^2}{3}+\frac{\left(m/2\right){\left(\frac{L}{2}\right)}^2}{3}=\frac{m{L}^2}{12}$