Question

A uniform thin rod of Length L and Mass M is bent at the middle point O. Consider an axis passing through its middle point O and perpendicular to the plane of the bent rod. The 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 $\frac{1}{12}m{L}^2$

Since the rod is bent at the middle point O, each part will have a mass of m/2 and length l/2.

So, moment of inertia about the point O = $\frac{1}{3}\frac{m}{2}(\frac{l}{2}{)}^2+\frac{1}{3}\frac{m}{2}(\frac{l}{2}{)}^2=\frac{1}{12}m{l}^2$