A smooth wire of length \( 2 \pi r \) is bent into a circle and kept in a vertical plane. A bead...

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A smooth wire of length \( 2 \pi r \) is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed \( \omega \) about the vertical diameter \( A B \) as shown in figure, the bead is at rest with respect to the circular ring at position \( P \) as shown. Then the value of \( \omega^{2} \) is equal to
[JEE (Main) 2019]
(a) \( \frac{2 g}{r} \)
(b) \( \frac{\sqrt{3} g}{2 r} \)
(c) \( \frac{(g \sqrt{3})}{r} \)
(d) \( \frac{2 g}{r \sqrt{3}} \)
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