Exam-Style Problem
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June 2011 p41 q3
3678
A small smooth ring R of weight 8.5 N is threaded on a light inextensible string. The ends of the string are attached to fixed points A and B, with A vertically above B. A horizontal force of magnitude 15.5 N acts on R so that the ring is in equilibrium with angle ARB = 90°. The part AR of the string makes an angle \(\theta\) with the horizontal and the part BR makes an angle \(\theta\) with the vertical (see diagram). The tension in the string is \(T\) N. Show that \(T \sin \theta = 12\) and \(T \cos \theta = 3.5\) and hence find \(\theta\).
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