6 Two uniform rods \(A B\) and \(B C\), each of length \(2 l\), are freely jointed at \(B\). The weight of \(A B\) is \(W\) and the weight of \(B C\) is \(2 W\). The rods are in a vertical plane with \(A\) freely pivoted at a fixed point and \(C\) resting in equilibrium on a rough horizontal plane. The normal and frictional components of the force acting on \(B C\) at \(C\) are \(R\) and \(F\) respectively. The rod \(A B\) makes an angle \(30 ^ { \circ }\) to the horizontal and the rod \(B C\) makes an angle \(60 ^ { \circ }\) to the horizontal (see diagram).
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1. By considering the equilibrium of \(\operatorname { rod } B C\), show that \(W + \sqrt { 3 } F = R\).
2. By taking moments about \(A\) for the equilibrium of the whole system, find another equation involving \(W , F\) and \(R\).
3. Given that the friction at \(C\) is limiting, calculate the value of the coefficient of friction at \(C\).