A beam $$\(A D C B\)$$ has length $$\(5 \mathrm{~m}\)$$. The beam lies on a horizontal step with the end $$\(A\)$$ on the step and the end $$\(B\)$$ projecting over the edge of the step. The edge of the step is at the point $$\(D\)$$ where $$\(D B=1.3 \mathrm{~m}\)$$, as shown in Figure 2. When a small boy of mass $$\(30 \mathrm{~kg}\)$$ stands on the beam at $$\(C\)$$, where $$\(C B=0.5 \mathrm{~m}\)$$, the beam is on the point of tilting. The boy is modelled as a particle and the beam is modelled as a uniform rod. (a) Find the mass of the beam. (3) A block of mass $$\(X \mathrm{~kg}\)$$ is now placed on the beam at $$\(A\)$$. The block is modelled as a particle. (b) Find the smallest value of $$\(X\)$$ that will enable the boy to stand on the beam at $$\(B\)$$ without the beam tilting. (3) (c) State how you have used the modelling assumption that the block is a particle in your calculations. (1)

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