A uniform $$\(\operatorname{rod} A B\)$$ has length $$\(5 \mathrm{~m}\)$$ and mass $$\(5 \mathrm{~kg}\)$$. The rod rests in equilibrium in a horizontal position on two supports $$\(C\)$$ and $$\(D\)$$, where $$\(A C=1 \mathrm{~m}\)$$ and $$\(D B=2 \mathrm{~m}\)$$, as shown in Figure 2. A particle of mass $$\(10 \mathrm{~kg}\)$$ is placed on the rod at $$\(A\)$$ and a particle of mass $$\(M \mathrm{~kg}\)$$ is placed on the rod at $$\(B\)$$. The rod remains horizontal and in equilibrium. (a) Find, in terms of $$\(M\)$$, the magnitude of the reaction on the rod at $$\(C\)$$. (3) (b) Find, in terms of $$\(M\)$$, the magnitude of the reaction on the rod at $$\(D\)$$. (3) (c) Hence, or otherwise, find the range of possible values of $$\(M\)$$. (3)

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