Question

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 the center of each sphere. Which one of the following statements concerning the moments of inertia of these spheres is true?

Answer 1

Answer:

Sphere B has 4 times more inertia than sphere A.

Explanation:

Inertia on a Solid sphere is given by:

$I = 2/5*M*R^2$

For this problem:

ma = mb = M

Rb = 2*Ra

With these values:

$Ia = 2/5*M*Ra^2$

$Ib = 2/5*M*(2*Ra)^2 = 4* (2/5*M*Ra^2)$

As you can see, Ib = 4 * Ia.