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Four identical point masses, each of mass m, are located at the four vertices of a square ABCD whose side length is ℓ. The moment of inertia of this arrangement about a line through A and parallel to the diagonal BD is

1. 2mℓ²
2. 3mℓ²
3. √3 mℓ²
4. mℓ²

Correct answer: 3mℓ²

Solution

Place A(0,0),B(l,0),C(l,l),D(0,l). The line through A parallel to BD is x+y=0; distance of a point is |x+y|/sqrt2. Contributions: A 0, B m*l^2/2, D m*l^2/2, C m*(2l^2). Total = 3 m l^2.

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