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

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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 \(\mathrm{AB}\), as shown in figure, the bead is at rest with respect to the circular ring at position $\mathrm{P}$ as shown. Then the value of \(\omega^2\) is equal to :
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