A uniform $$\(\operatorname{rod} A B\)$$ has length $$\(2 a\)$$ and mass $$\(M\)$$. The rod is held in equilibrium in a horizontal position by two vertical light strings which are attached to the rod at $$\(C\)$$ and $$\(D\)$$, where $$\(A C=\frac{2}{5} a\)$$ and $$\(D B=\frac{3}{5} a\)$$, as shown in Figure 1 A particle $$\(P\)$$ is placed on the rod at $$\(B\)$$. The rod remains horizontal and in equilibrium. (a) Find, in terms of $$\(M\)$$, the largest possible mass of the particle $$\(P\)$$ (3) Given that the mass of $$\(P\)$$ is $$\(\frac{1}{2} M\)$$ (b) find, in terms of $$\(M\)$$ and $$\(g\)$$, the tension in the string that is attached to the rod at $$\(C\)$$. (3)

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