A particle \(P\) of mass \(0.05\,\text{kg}\) is attached to one end of a light inextensible string of length \(1\) m. The other end is attached to a fixed point \(O\). A particle \(Q\) of mass \(0.04\,\text{kg}\) is attached to one end of a second light inextensible string, whose other end is attached to \(P\).

The particle \(P\) moves in a horizontal circle of radius \(0.8\) m with angular speed \(\omega\,\text{rad s}^{-1}\). The particle \(Q\) moves in a horizontal circle of radius \(1.4\) m with the same angular speed. The centres of the circles are vertically below \(O\), and \(O\), \(P\), and \(Q\) are always in the same vertical plane. The strings \(OP\) and \(PQ\) make constant angles \(\alpha\) and \(\beta\) respectively with the vertical.

(a) Find the tension in the string \(OP\).

(b) Find \(\omega\).

(c) Find \(\beta\).