Question

How does a uniform solid sphere’s moment of inertia, I, change if its mass is tripled and its radius is doubled?

A) increases by a factor of 6
B) increases by a factor of 54
C) increases by a factor of 18
D) increases by a factor of 12
E) increases by a factor of 5

Answer 1

The moment of inertia of a uniform solid sphere increases by a factor of 4 if its mass is tripled and its radius is doubled.

Step-by-step explanation:

The moment of inertia, I, of a solid sphere is given by the equation I = (2/5)mr^2, where m is the mass of the sphere and r is the radius. If the mass is tripled, the new mass is 3m. If the radius is doubled, the new radius is 2r. Substituting these values into the equation, we get I' = (2/5)(3m)(2r)^2 = (2/5)(3)(4)(m)(r^2) = 4I. Therefore, the moment of inertia increases by a factor of 4.