4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{266c4f52-f35f-459c-9184-836b0f3baf5b-12_609_639_296_657}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A uniform rod \(A B\) has mass 5 kg and length 4 m . The rod is held in a horizontal position by a light inextensible string. The end \(A\) of the rod rests against a rough vertical wall. One end of the string is attached to the rod at \(B\) and the other end is attached to the wall at a point \(D\). The point \(D\) is vertically above \(A\), with \(A D = 3 \mathrm {~m}\). A particle of mass 2 kg is attached to the rod at \(C\), where \(A C = 0.5 \mathrm {~m}\), as shown in Figure 1. The rod is in equilibrium in a vertical plane perpendicular to the wall. The coefficient of friction between the rod and the wall is \(\mu\).
Find
- the tension in the string,
- the magnitude of the force exerted by the wall on the rod at \(A\),
- the range of possible values of \(\mu\).