One end of a light inextensible string of length \(a\) is attached to a fixed point \(O\). The other end of the string is attached to a particle of mass \(m\). The string is taut and makes an angle \(\theta\) with the downward vertical through \(O\), where \(\cos\theta=\dfrac23\). The particle moves in a horizontal circle with speed \(v\).

Find \(v\) in terms of \(a\) and \(g\).