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ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. I_AB, I_BC and I_CA are the moments of inertia of the plate about AB, BC and CA as axes respectively. Which one of the following relations is correct?

1. I_AB > I_BC
2. I_BC > I_AB
3. I_AB + I_BC = I_CA
4. I_CA is maximum

Correct answer: I_BC > I_AB

Solution

The moment of inertia of a triangular plate depends on the distribution of mass relative to the axis. Since BC is the longest side, the mass distribution is farther from BC compared to AB, making I_BC > I_AB.

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