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The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I₀. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

1. I₀ + ML²/2
2. I₀ + ML²/4
3. I₀ + 2 ML²
4. I₀ + ML²

Correct answer: I₀ + ML²/2

Solution

Using the parallel axis theorem, the moment of inertia about an axis passing through one end is I = I₀ + Md², where d = L/2. Substituting, we get I = I₀ + M(L/2)² = I₀ + ML²/4.

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