6 A uniform \(\operatorname { rod } A B\), of weight \(W\) and length \(2 l\) is in equilibrium at \(60 ^ { \circ }\) to the horizontal with \(A\) resting against a smooth vertical plane and \(B\) resting on a rough section of a horizontal plane. Another uniform rod \(C D\), of length \(\sqrt { 3 } l\) and weight \(W\), is freely jointed to the mid-point of \(A B\) at \(C\); its other end \(D\) rests on a smooth section of the horizontal plane. \(C D\) is inclined at \(30 ^ { \circ }\) to the horizontal (see diagram).
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1. Show that the force exerted by the horizontal plane on \(C D\) is \(\frac { 1 } { 2 } W\). Find the normal component of the force exerted by the horizontal plane on \(A B\).
2. Find the magnitude and direction of the force exerted by \(C D\) on \(A B\).
3. Given that \(A B\) is in limiting equilibrium, find the coefficient of friction between \(A B\) and the horizontal plane.