A uniform wire \(A B C D\) is bent into the shape shown, where the sections \(A B , B C\) and \(C D\) are straight and of length \(3 a , 10 a\) and \(5 a\) respectively and \(A D\) is parallel to \(B C\).
Show that the cosine of angle \(B C D\) is \(\frac { 4 } { 5 }\).
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Find the distances of the centre of mass of the bent wire from (i) \(A B\), (ii) \(B C\).
The wire is hung over a smooth peg at \(B\) and rests in equilibrium.
Find, to the nearest \(0.1 ^ { \circ }\), the angle between \(B C\) and the vertical in this position.