6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{184043b7-1222-44fb-bc9f-3f484f72147b-16_458_798_258_630}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
Figure 5 shows a uniform rod \(A B\) of mass \(M\) and length \(2 a\).
- the rod has its end \(A\) on rough horizontal ground
- the rod rests in equilibrium against a small smooth fixed horizontal peg \(P\)
- the point \(C\) on the rod, where \(A C = 1.5 a\), is the point of contact between the rod and the peg
- the rod is at an angle \(\theta\) to the ground, where \(\tan \theta = \frac { 4 } { 3 }\)
The rod lies in a vertical plane perpendicular to the peg.
The magnitude of the normal reaction of the peg on the rod at \(C\) is \(S\).
- Show that \(S = \frac { 2 } { 5 } M g\)
The coefficient of friction between the rod and the ground is \(\mu\).
Given that the rod is in limiting equilibrium, - find the value of \(\mu\).