Question

A thin rod of length $L$ and mass $M$ is bent at the middle point $O$ at an angle of $60^{\circ} .$ 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)

Moment of inertia of a uniform rod about one end
$=\frac{m l^{2}}{3}$
$\therefore $ Moment of inertia of the system, which rod is bent,
$=2 \times\left(\frac{M}{2}\right) \frac{(L / 2)^{2}}{3}=\frac{M L^{2}}{12}$