Answer
The moment of inertia of sphere 2 exceeds the moment of inertia of sphere 1 by a factor of 32
Work Step by Step
Let the mass of sphere 1 be $M$. Let the radius of sphere 1 be $R$. We can find the moment of inertia of sphere 1 as:
$I_1 = \frac{2}{5}MR^2$
Sphere 2 has twice the radius of sphere 1. Therefore, sphere 2 has 8 times the volume of sphere 1 and so it has 8 times the mass of sphere 1. We can find the moment of inertia of sphere 2 as:
$I_2 = \frac{2}{5}(8M)(2R)^2$
$I_2 = 32\times (\frac{2}{5}MR^2)$
$I_2 = 32\times I_1$
Therefore, the moment of inertia of sphere 2 exceeds the moment of inertia of sphere 1 by a factor of 32.
