4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5ef8231d-5b95-4bbb-a8e2-788c708fa078-12_518_696_319_625}
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\caption{Figure 1}
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A uniform \(\operatorname { rod } A B\) has mass \(m\) and length \(6 a\). The end \(A\) rests against a rough vertical wall. One end of a light inextensible string is attached to the rod at the point \(C\), where \(A C = 2 a\). The other end of the string is attached to the wall at the point \(D\), where \(D\) is vertically above \(A\), with the string perpendicular to the rod. A particle of mass \(m\) is attached to the rod at the end \(B\). The rod is in equilibrium in a vertical plane which is perpendicular to the wall. The rod is inclined at \(60 ^ { \circ }\) to the wall, as shown in Figure 1.
Find, in terms of \(m\) and \(g\),
- the tension in the string,
- the magnitude of the horizontal component of the force exerted by the wall on the rod.
The coefficient of friction between the wall and the rod is \(\mu\). Given that the rod is in limiting equilibrium,
- find the value of \(\mu\).