3.
\begin{figure}[h]
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\caption{Figure 1}
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A uniform \(\operatorname { rod } A B\) of weight \(W\) is freely hinged at end \(A\) to a vertical wall. The rod is supported in equilibrium at an angle of \(60 ^ { \circ }\) to the wall by a light rigid strut \(C D\). The strut is freely hinged to the rod at the point \(D\) and to the wall at the point \(C\), which is vertically below \(A\), as shown in Figure 1. The rod and the strut lie in the same vertical plane, which is perpendicular to the wall. The length of the rod is \(4 a\) and \(A C = A D = 2.5 a\).
- Show that the magnitude of the thrust in the strut is \(\frac { 4 \sqrt { 3 } } { 5 } W\).
- Find the magnitude of the force acting on the \(\operatorname { rod }\) at \(A\).