A particle \(P\) of mass \(m\) is attached to one end of a light inextensible string of length \(a\). The other end is attached to a fixed point \(O\). The particle is held at point \(A\) with the string taut.

The line \(OA\) makes an angle \(\theta\) with the downward vertical through \(O\), where \(\tan\theta=\dfrac34\). The particle is projected perpendicular to \(OA\) in an upwards direction with speed \(\sqrt{5ag}\), and it starts to move along a circular path in a vertical plane.

When \(P\) is at point \(B\), where \(\angle AOB=90^\circ\), the tension in the string is \(T\). Find \(T\) in terms of \(m\) and \(g\).