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, then bead is at rest with respect to the circular ring at position P as shown (i.e P is moving in a circle of radius r/2). Then the value of ${\omega }^2$ is equal to ($g=10m/s^2$ )