A small bead can slide without friction on a circular wire ring of radius $20\ \text{cm}$. The ring stands in a vertical plane and spins about its vertical diameter at $10\ \text{rad/s}$, as shown in the figure. Taking $g = 10\ \text{m/s}^2$, at what angle from the lowest point of the ring (measured at the centre) can the bead stay at rest relative to the ring, apart from the bottom itself?

Fig. 1: A vertical circular ring of radius 20 cm spinning at 10 rad/s about its vertical diameter, with a bead on the ring at an angle theta from the lowest point, measured at the centre.