Question

The moment of inertia of a rod about an axis passing through its centre and perpendicular to its length is \[ I=\frac{1}{12}ML^2, \] where \(M\) is the mass and \(L\) is the length of the rod. The rod is bent in the middle so that the two halves make an angle of \(60^\circ\). The moment of inertia of the bent rod about the same axis would be

• A. \[ \frac{1}{12}ML^2 \]
• B. \[ \frac{1}{8\sqrt3}ML^2 \]
• C. \[ \frac{1}{24}ML^2 \]
• D. \[ \frac{1}{48}ML^2 \]

Hint:

For an axis perpendicular to the plane through the bend point, the moment of inertia depends only on the distances of mass elements from the axis. Bending the rod changes direction but not these distances, so the moment of inertia remains unchanged.

Answer 1

The Correct Option is A