A uniform rod, of length $$\(8 a\)$$ and mass $$\(M\)$$, has one end freely hinged to a fixed point $$\(A\)$$ on a vertical wall. One end of a light inextensible string is attached to the rod at the point $$\(B\)$$, where $$\(A B=5 a\)$$. The other end of the string is attached to the wall at the point $$\(C\)$$, where $$\(A C=5 a\)$$ and $$\(C\)$$ is vertically above $$\(A\)$$. The rod rests in equilibrium in a vertical plane perpendicular to the wall with angle $$\(B A C=70^{\circ}\)$$, as shown in Figure 3. (a) Find, in terms of $$\(M\)$$ and $$\(g\)$$, the tension in the string. (3) The magnitude of the force acting on the rod at $$\(A\)$$ is $$\(\lambda M g\)$$, where $$\(\lambda\)$$ is a constant. (b) Find, to 2 significant figures, the value of $$\(\lambda\)$$. (6)

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