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From the figure, calculate the total moment of inertia of the rod when I is minimum.

1. I = m₁x² + m₂(L − x)²
2. I = m₁x² + m₂L² − 2Lx
3. I = m₁x² + m₂L² − m₂Lx
4. I = m₁x² + m₂L² − 2m₂Lx

Correct answer: I = m₁x² + m₂L² − 2m₂Lx

Solution

The total moment of inertia is calculated by summing the contributions of both masses. The term involving 'x' and 'L' simplifies to the correct expression in option D, which accounts for the minimum moment of inertia condition.

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