Two uniform solid spheres, A and B have the same mass. The radius of sphere B is twice that of sphere A. The axis of rotation passes through each sphere. Which one of the following statements concerning the moments of inertia of these spheres is true?
A)The moment of inertia of A is one-fourth that of B.
B)The moment of inertia of A is one-half that of B.
C)The moment of inertia of A is 5/4 that of B.
D)The moment of inertia of A is 5/2 that of B.
E)The two spheres have equal moments of inertia.

Question

Quizplus · Accepted Answer

The moment of inertia of a solid sphere is given by (2/5)mr^2, where m is the mass and r is the radius. Since the mass of both spheres is the same, the moment of inertia of sphere A is (2/5)m(r_A^2), and the moment of inertia of sphere B is (2/5)m(r_B^2), where r_B = 2r_A. Therefore, the moment of inertia of sphere A is (2/5)m(r_A^2), and the moment of inertia of sphere B is (2/5)m(4r_A^2) = (8/5)m(r_A^2). Dividing these two equations, we get the moment of inertia of A to B as (2/5)m(r_A^2)/(8/5)m(r_A^2) = 1/4. Thus, the moment of inertia of A is one-fourth that of B, which is choice A.

Two Uniform Solid Spheres, a and B Have the Same