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:
(1) $2 \mathrm {~g} / \mathrm { r }$
(2) $\frac { \sqrt { 3 } \mathrm {~g} } { 2 \mathrm { r } }$
(3) $2 g / ( r \sqrt { 3 } )$
(4) $( \mathrm { g } \sqrt { 3 } ) / \mathrm { r }$