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A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then the relation between the moment of inertia Iₓ and I_y is

1. I_y = 32 Iₓ
2. I_y = 16 Iₓ
3. I_y = Iₓ
4. I_y = 64 Iₓ

Correct answer: I_y = 64 Iₓ

Solution

The moment of inertia for a disc is proportional to its mass and the square of its radius. Disc Y, having a radius 4R and a thickness t/4, has a mass that scales with the volume, resulting in a factor of 16 increase due to the radius squared and an additional factor of 4 due to the thickness, leading to a total increase of 64 times the moment of inertia of disc X.

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