The spool shown in the figure is placed on a rough horizontal surface and has an inner radius $r$ and an outer radius $R$. The angle $\theta$ between the applied force and the horizontal can be varied. The critical angle $\theta$ for which the spool does not roll and remains stationary is given by:

• A
  $\theta = \cos^{-1} \left( \frac{r}{R} \right)$
• B
  $\theta = \cos^{-1} \left( \frac{2r}{R} \right)$
• C
  $\theta = \cos^{-1} \sqrt{\frac{r}{R}}$
• D
  $\theta = \sin^{-1} \left( \frac{r}{R} \right)$