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A triangular lamina has sides of length a, b, and c, and its moment of inertia about the side of length a is I₀. A second triangular lamina is geometrically similar, with sides 2a, 2b, and 2c. What is the moment of inertia of the second lamina about the side of length 2a? (Assume both laminas are made of the same material with the same thickness.)

1. 2*I₀
2. 4*I₀
3. 8*I₀
4. 16*I₀

Correct answer: 16*I₀

Solution

Scaling all linear dimensions by k = 2 increases the mass by k² = 4 and each moment arm by k = 2, so the MI scales by k⁴ = 16, giving I_new = 16*I₀.

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