7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c5760fa5-3c7f-4e29-87a2-b3b4145b9361-14_442_986_264_479}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
A uniform plank \(A B\), of weight 100 N and length 4 m , rests in equilibrium with the end \(A\) on rough horizontal ground. The plank rests on a smooth cylindrical drum. The drum is fixed to the ground and cannot move. The point of contact between the plank and the drum is \(C\), where \(A C = 3 \mathrm {~m}\), as shown in Figure 4. The plank is resting in a vertical plane which is perpendicular to the axis of the drum, at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 3 }\). The coefficient of friction between the plank and the ground is \(\mu\). Modelling the plank as a rod, find the least possible value of \(\mu\).