Answer
$\theta = 8.0^{\circ}$
Work Step by Step
We can write an expression for the rotational inertia of a solid sphere:
$I = \frac{2}{5}MR^2$
We can use Equation (11-10) to find the incline angle $\theta$:
$a = \frac{g~sin~\theta}{1+I/MR^2}$
$a = \frac{g~sin~\theta}{1+\frac{2}{5}MR^2/MR^2}$
$a = \frac{g~sin~\theta}{1+\frac{2}{5}}$
$a = \frac{5}{7}~g~sin~\theta = 0.10~g$
$sin~\theta = \frac{0.7}{5}$
$\theta = sin^{-1}~(\frac{0.7}{5})$
$\theta = 8.0^{\circ}$
