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A cube of the largest possible size is carved out from a solid sphere having mass M and radius R. The moment of inertia of this cube about an axis through its centre and normal to one of its faces is:

1. 4MR²/(9√3π)
2. 4MR²/(3√3π)
3. MR²/(32√2π)
4. MR²/(16√2π)

Correct answer: 4MR²/(9√3π)

Solution

Largest inscribed cube has a = 2R/sqrt3. Cube mass = M*(a^3)/((4/3)pi R^3) = 2M/(sqrt3 pi). I about axis normal to a face = (1/6) m a^2 = (1/6)*(2M/(sqrt3 pi))*(4R^2/3) = 4MR^2/(9 sqrt3 pi).

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