A ring of weight \(W\), radius \(a\) and centre \(O\), is at rest on a rough surface inclined at an angle \(\alpha\) to the horizontal, where \(\tan\alpha=\dfrac12\). The plane of the ring is perpendicular to the inclined surface and parallel to a line of greatest slope.

The point \(P\) on the circumference is such that \(OP\) is parallel to the surface. A light inextensible string is attached to \(P\) and to a point \(Q\) on the surface so that \(PQ\) is horizontal. The points \(O\), \(P\) and \(Q\) are in the same vertical plane. The system is in limiting equilibrium and the coefficient of friction between the ring and the surface is \(\mu\).

(a) Find, in terms of \(W\), the tension in the string \(PQ\).

(b) Find \(\mu\).