4 A uniform rod \(A B\), of length \(2 a\) and mass \(2 m\), can rotate freely in a vertical plane about a smooth horizontal axis through \(A\). A small rough ring of mass \(m\) is threaded on the rod. The rod is held in a horizontal position with the ring at rest at the mid-point of the rod. The rod is released from rest. Using energy considerations, show that, until the ring slides, $$a \dot { \theta } ^ { 2 } = \frac { 18 } { 11 } g \sin \theta$$ where \(\theta\) is the angle turned through by the rod. Show that, until the ring slides, the magnitudes of the friction force and normal contact force acting on the ring are \(\frac { 29 } { 11 } m g \sin \theta\) and \(\frac { 2 } { 11 } m g \cos \theta\) respectively. The coefficient of friction between the ring and the rod is \(\mu\). Find, in terms of \(\mu\), the value of \(\theta\) when the ring starts to slide.