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

Question

A thin rod of length L and mass M is bent at the middle point O at an angle of 60° . The moment of inertia of the rod about an axis passing through O and perpendicular to the plane of the rod will be (A) (M L2/6) (B) (M L2/12) (C) (M L2/24) (D) (M L2/3)

Tardigrade Admin · Accepted Answer

Moment of inertia of a uniform rod about one end =(m l2/3) ∴ Moment of inertia of the system, which rod is bent, =2 ×((M/2)) ((L / 2)2/3)=(M L2/12)

Q. A thin rod of length $L$ and mass $M$ is bent at the middle point $O$ at an angle of $6 0^{\circ} .$ The moment of inertia of the rod about an axis passing through $O$ and perpendicular to the plane of the rod will be

$\frac{M L ^{2}}{6}$

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

$\frac{M L ^{2}}{24}$

$\frac{M L ^{2}}{3}$

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

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

6ML2​

12ML2​

24ML2​

3ML2​