2 A uniform \(\operatorname { rod } A B\) of weight \(W\) rests in equilibrium with \(A\) in contact with a rough vertical wall. The rod is in a vertical plane perpendicular to the wall, and is supported by a force of magnitude \(P\) acting at \(B\) in this vertical plane. The rod makes an angle of \(60 ^ { \circ }\) with the wall, and the force makes an angle of \(30 ^ { \circ }\) with the rod (see diagram). Find the value of \(P\). Find also the set of possible values of the coefficient of friction between the rod and the wall.