5
\includegraphics[max width=\textwidth, alt={}, center]{20dd0f90-8c10-4a7b-a383-4ba89d167cd6-3_716_549_269_799} Two uniform rods, \(A B\) and \(B C\), each have length \(2 a\) and weight \(W\). They are smoothly jointed at \(B\), and \(A\) is attached to a smooth fixed pivot. A light inextensible string of length ( \(2 \sqrt { } 2\) ) \(a\) joins \(A\) to \(C\) so that angle \(A B C = 90 ^ { \circ }\). The system hangs in equilibrium, with \(A B\) making an angle \(\alpha\) with the vertical (see diagram). By taking moments about \(A\) for the system, or otherwise, show that \(\alpha = 18.4 ^ { \circ }\), correct to the nearest \(0.1 ^ { \circ }\). Find the tension in the string in the form \(k W\), giving the value of \(k\) correct to 3 significant figures. Find, in terms of \(W\), the magnitude of the force acting on the \(\operatorname { rod } B C\) at \(B\).