1 A particle \(P\) of mass \(m\) is attached to one end of a light inextensible string of length \(a\). The other end of the string is attached to a fixed point \(O\) on a smooth horizontal plane. The particle \(P\) moves in horizontal circles about \(O\). The tension in the string is \(4 m g\). Find, in terms of \(a\) and \(g\), the time that \(P\) takes to make one complete revolution.