Two uniform solid spheres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia about a central axis to that of the smaller sphere is
A) 2.
B) 4.
C) 4/5.
D) 8/5.
E) 1/2.

Question

Quizplus · Accepted Answer

The moment of inertia of a solid sphere about a central axis is given by I = (2/5)MR^2, where M is the mass and R is the radius. Since the two spheres have the same mass, the ratio of their moments of inertia is equal to the ratio of their radii squared. Therefore, the ratio of the larger sphere's moment of inertia to that of the smaller sphere is (2R)^2/R^2 = 4.

Two Uniform Solid Spheres Have the Same Mass, but One