A ball of mass \( m \) is attached to the end of a thread fastened to the top of a vertical rod ...

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A ball of mass \( m \) is attached to the end of a thread fastened to the top of a vertical rod which is fitted to a horizontally revolving round table as shown. If the thread forms an angle \( \alpha \) with the vertical, the angular velocity \( \omega \) of table is
(1) \( \sqrt{\frac{g}{1 \cos \alpha}} \)
(2) \( \sqrt{\frac{r}{g \tan \alpha}} \)
(3) \( \sqrt{\frac{g \tan \alpha}{r+l \sin \alpha}} \)
(4) \( \sqrt{\frac{g \tan \alpha}{r}} \)
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