2. A rod \(A B\) has mass \(m\) and length \(4 a\). It is free to rotate about a fixed smooth horizontal axis through the point \(O\) of the rod, where \(A O = a\). The rod is hanging in equilibrium with \(B\) below \(O\) when it is struck by a particle \(P\), of mass \(3 m\), moving horizontally with speed \(v\). When \(P\) strikes the rod, it adheres to it. Immediately after striking the rod, \(P\) has speed \(\frac { 2 } { 3 } v\). Find the distance from \(O\) of the point where \(P\) strikes the rod.
(7 marks)