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A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90°. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is:

1. ML²/24
2. ML²/12
3. ML²/6
4. √2 ML²/6

Correct answer: ML²/12

Solution

The rod is bent into two equal halves, each of length L/2. The moment of inertia of each half about the given axis is (1/3)ML²/4 (using the formula for a rod about one end). Adding the contributions of both halves gives ML²/12.

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