Answer
The radius of gyration:
${r_g} = \sqrt {\frac{2}{5}} R$
Work Step by Step
From Exercise 43, we obtain the moment of inertia of any axis that passes through the center of the sphere with uniform mass density is $I = \frac{2}{5}M{R^2}$.
By definition, the radius of gyration is given by
${r_g} = {\left( {\frac{I}{M}} \right)^{1/2}} = \sqrt {\frac{2}{5}} R$
