$$\(\quad\)$$ The centre of mass of a semicircular arc of radius $$\(r\)$$ is $$\(\frac{2 r}{\pi}\)$$ from the centre.] Uniform wire is used to form the framework shown in Figure 2. In the framework, - $$\(A B C\)$$ is straight and has length $$\(25 a\)$$ - $$\(A D E\)$$ is straight and has length $$\(24 a\)$$ - $$\(A B D\)$$ is a semicircular arc of radius $$\(7 a\)$$ - $$\(E C=7 a\)$$ - angle $$\(A E C=90^{\circ}\)$$ - the points $$\(A, B, C, D\)$$ and $$\(E\)$$ all lie in the same plane The distance of the centre of mass of the framework from $$\(A E\)$$ is $$\(d\)$$. (a) Show that $$\(d=\frac{53}{2(7+\pi)} a\)$$ (4) The framework is freely suspended from $$\(A\)$$ and hangs in equilibrium with $$\(A C\)$$ at angle $$\(\alpha^{\circ}\)$$ to the downward vertical. (b) Find the value of $$\(\alpha\)$$. (7)

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