1 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 \(\cos \theta = \frac { 2 } { 3 }\). The particle moves in a horizontal circle with speed \(v\). Find \(v\) in terms of \(a\) and \(g\).
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