The end \(A\) of a uniform rod \(AB\), of length \(6a\) and weight \(W\), is in contact with a rough vertical wall. One end of a light inextensible string of length \(3a\) is attached to the midpoint \(C\) of the rod. The other end is attached to a point \(D\) on the wall, vertically above \(A\).

The rod is in equilibrium when the angle between the rod and the wall is \(\theta\), where \(\tan\theta=\dfrac32\). A particle of weight \(W\) is attached to the point \(E\) on the rod, where \(AE=ka\), with \(3\lt k\lt6\). The coefficient of friction between the rod and the wall is \(\dfrac13\). The rod is about to slip down the wall.

(a) Find \(k\).

(b) Find, in terms of \(W\), the magnitude of the frictional force between the rod and the wall.