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The spool shown in the figure is placed on a rough horizontal
P surface and has inner radius \( r \) and outer radius \( R \). The angle

W \( \theta \) 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
(1) \( \theta=\cos ^{-1}\left(\frac{r}{R}\right) \)
(2) \( \theta=\cos ^{-1}\left(\frac{2 r}{R}\right) \)
(3) \( \theta=\cos ^{-1} \sqrt{\frac{r}{R}} \)
(4) \( \theta=\sin ^{-1}\left(\frac{r}{R}\right) \)
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