Question

A thin rod of length $L$ and mass $M$ is bent at the middle point O at an angle of ${60}^o$. The moment of inertia of the rod about an axis passing through O and perpendicular to the plane of the rod will be:

• A. $\frac{M{L}^2}{6}$
• B. $\frac{M{L}^2}{12}$
• C. $\frac{M{L}^2}{24}$
• D. $\frac{M{L}^2}{3}$

Answer 1

Answer: (B)

$\frac{M{L}^2}{12}$

When a rod is bend, then the mass of each half is $m=M/2$ and length $l=L/2$

MI of the road about the point O is $I=2\frac{m{l}^2}{3}$

So, $I=2\frac{\left(M/2\right)(L/2{)}^2}{3}=\frac{M{L}^2}{12}$