Two identical small rings, $$\(A\)$$ and $$\(B\)$$, each of mass $$\(m\)$$, are threaded onto a rough horizontal wire. The rings are connected by a light inextensible string. A particle $$\(C\)$$ of mass $$\(3 m\)$$ is attached to the midpoint of the string. The particle $$\(C\)$$ hangs in equilibrium below the wire with angle $$\(B A C=\beta\)$$, as shown in Figure 2. The tension in each of the parts, $$\(A C\)$$ and $$\(B C\)$$, of the string is $$\(T\)$$ (a) By considering particle $$\(C\)$$, find $$\(T\)$$ in terms of $$\(m, g\)$$ and $$\(\beta\)$$ (2) (b) Find, in terms of $$\(m\)$$ and $$\(g\)$$, the magnitude of the normal reaction between the wire and $$\(A\)$$. (3) The coefficient of friction between each ring and the wire is $$\(\frac{4}{5}\)$$ The two rings, $$\(A\)$$ and $$\(B\)$$, are on the point of sliding along the wire towards each other. (c) Find the value of $$\(\tan \beta\)$$ (5)

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