Two uniform solid spheres have masses M₀ and (1/2)M₀ and radii R₀ and (1/2)R₀ respectively. The ratio of their moments of inertia about their own diameters is A) 8:1. B) 4:1. C) 2:1. D) 1:1.

Question

Quizplus · Accepted Answer

The moment of inertia of a solid sphere about its diameter is given by (2/5)MR². For the first sphere, it is (2/5)M₀R₀². For the second sphere, it is (2/5)(1/2)M₀(1/2R₀)² = (2/5)(1/2)M₀(1/4)R₀² = (1/20)M₀R₀². The ratio is (2/5)M₀R₀² : (1/20)M₀R₀² = 8:1.

Two Uniform Solid Spheres Have Masses M0 and (1/2)M0 and Radii

Two Uniform Solid Spheres Have Masses M₀ and (1/2)M₀ and Radii