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 to that of the smaller sphere is
A) 4/5.
B) 8/5.
C) 1/2.
D) 2.
E) 4.

Question

Quizplus · Accepted Answer

The formula for the moment of inertia of a solid sphere is:
I = (2/5) mr^2
where I is the moment of inertia, m is the mass of the sphere, and r is the radius of the sphere.

Since the two spheres have the same mass, the larger sphere has a moment of inertia that is proportional to the square of its radius. Specifically, the ratio of the larger sphere's moment of inertia to that of the smaller sphere is:

I_large / I_small = (2/5) m(2r)^2 / (2/5) mr^2
= 8r^2 / r^2
= 8

Therefore, the answer is E) 4.

Two Uniform Solid Spheres Have the Same Mass, but One