6.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{f180f5f0-43c5-4365-b0d8-7284220b481e-20_593_745_246_667}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}

A uniform $\operatorname { rod } A B$ has length $8 a$ and weight $W$.\\
The end $A$ of the rod is freely hinged to a fixed point on a vertical wall.\\
A particle of weight $\frac { 1 } { 4 } W$ is attached to the rod at $B$.\\
A light inelastic string of length $5 a$ has one end attached to the rod at the point $C$, where $A C = 5 a$.

The other end of the string is attached to the wall at the point $D$, where $D$ is above $A$ and $A D = 5 a$, as shown in Figure 4.

The rod rests in equilibrium.\\
The tension in the string is $T$.
\begin{enumerate}[label=(\alph*)]
\item Show that $T = \frac { 6 } { 5 } \mathrm {~W}$
\item Find, in terms of $W$, the magnitude of the force exerted on the rod by the hinge at $A$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2023 Q6 [9]}}