# Chapter 12 - Rotation of a Rigid Body - Conceptual Questions: 6

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.

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