The moment of inertia of a rod about an axis through its centre and perpendicular to it is 12 1 M L 2 (where M is the mass and L , the length of the rod). The rod is bent in the middle so that the t

Question

The moment of inertia of a rod about an axis through its centre and perpendicular to it is 12 1 ​ M L 2 (where M is the mass and L , the length of the rod). The rod is bent in the middle so that the two halves make an angle of 6 0 ∘ . The moment of inertia of the bent rod about the same axis would be

TestHub · Accepted Answer

Moment of inertia of uniform rod about one end $= \frac{M L ^{2}}{3}$ . $∴$ Moment of inertia of a rod about an axis passing through $O$ and perpendicular to the plane of the rod will be $= 2 (\frac{M}{2}) \frac{( L /2 ) ^{2}}{3} = \frac{M L ^{2}}{4 \times 3} = \frac{M L ^{2}}{12}$

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