5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e6e37d85-f8de-490a-82a9-8a3c16e2fdd0-12_638_595_251_676}
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\caption{Figure 3}
\end{figure}
A uniform rod, of length \(8 a\) and mass \(M\), has one end freely hinged to a fixed point \(A\) on a vertical wall. One end of a light inextensible string is attached to the rod at the point \(B\), where \(A B = 5 a\). The other end of the string is attached to the wall at the point \(C\), where \(A C = 5 a\) and \(C\) is vertically above \(A\). The rod rests in equilibrium in a vertical plane perpendicular to the wall with angle \(B A C = 70 ^ { \circ }\), as shown in Figure 3.
- Find, in terms of \(M\) and \(g\), the tension in the string.
The magnitude of the force acting on the rod at \(A\) is \(\lambda M g\), where \(\lambda\) is a constant.
- Find, to 2 significant figures, the value of \(\lambda\).