- A rough circular cylinder of radius \(4 a\) is fixed to a rough horizontal plane with its axis horizontal. A uniform rod \(A B\), of weight \(W\) and length \(6 a \sqrt { 3 }\), rests with its lower end \(A\) on the plane and a point \(C\) of the rod against the cylinder. The vertical plane through the rod is perpendicular to the axis of the cylinder. The rod is inclined at \(60 ^ { \circ }\) to the horizontal, as shown in Figure 1.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2226b09b-a19d-4253-baaa-3c3d602d0d6d-06_389_862_482_550}
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\caption{Figure 1}
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- Show that \(A C = 4 a \sqrt { } 3\)
The coefficient of friction between the rod and the cylinder is \(\frac { \sqrt { } 3 } { 3 }\) and the coefficient of friction between the rod and the plane is \(\mu\). Given that friction is limiting at both \(A\) and \(C\),
- find the value of \(\mu\).