6
\includegraphics[max width=\textwidth, alt={}, center]{ce4c43e6-da4f-4c02-ab0f-01a21717949c-3_348_1109_1345_516} A small smooth ring \(R\) of weight 7 N is threaded on a light inextensible string. The ends of the string are attached to fixed points \(A\) and \(B\) at the same horizontal level. A horizontal force of magnitude 5 N is applied to \(R\). The string is taut. In the equilibrium position the angle \(A R B\) is a right angle, and the portion of the string attached to \(B\) makes an angle \(\theta\) with the horizontal (see diagram).

1. Explain why the tension \(T \mathrm {~N}\) is the same in each part of the string.
2. By resolving horizontally and vertically for the forces acting on \(R\), form two simultaneous equations in \(T \cos \theta\) and \(T \sin \theta\).
3. Hence find \(T\) and \(\theta\).