4.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{266c4f52-f35f-459c-9184-836b0f3baf5b-12_609_639_296_657}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\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
\begin{enumerate}[label=(\alph*)]
\item the tension in the string,
\item the magnitude of the force exerted by the wall on the rod at $A$,
\item the range of possible values of $\mu$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2017 Q4 [11]}}