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 AB, 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 -

Question

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 AB, 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 -

${{\sqrt 3 g} \over {2r}}$

${{2g} \over {\left( {r\sqrt 3 } \right)}}$

${{\left( {g\sqrt 3 } \right)} \over r}$

${{2g} \over r}$

Solution

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