A uniform rod, $$\(A B\)$$, of weight $$\(W\)$$ and length $$\(8 a\)$$, rests in equilibrium with the end $$\(A\)$$ on rough horizontal ground. The rod rests on a smooth cylinder. The cylinder is fixed to the ground with its axis horizontal. The point of contact between the rod and the cylinder is $$\(C\)$$, where $$\(A C=7 a\)$$, as shown in Figure 4. The rod is resting in a vertical plane that is perpendicular to the axis of the cylinder. The rod makes an angle $$\(\alpha\)$$ with the horizontal. (a) Show that the normal reaction of the ground on the $$\(\operatorname{rod}\)$$ at $$\(A\)$$ has magnitude $$\(W\left(1-\frac{4}{7} \cos ^{2} \alpha\right)\)$$ (6) Given that the coefficient of friction between the rod and the ground is $$\(\mu\)$$ and that $$\(\cos \alpha=\frac{3}{\sqrt{10}}\)$$ (b) find the range of possible values of $$\(\mu\)$$. (5)

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