The diagram below shows a spotlight system that consists of a symmetrical track $XY$ that is suspended horizontally from the ceiling by means of two vertical wires.

\includegraphics{figure_9}

Each of the three spotlights $A$, $B$, $C$ may be moved horizontally along its corresponding shaded section of the track. The system remains in equilibrium.

The track may be modelled as a light uniform rod of length $1.8$ m and the wires are fixed at a distance of $0.4$ m from each end. Each of the spotlights may be modelled as a particle of mass $m$ kg, positioned at the points where they are in contact with the track.

The distances of the spotlights relative to the wires are given in the diagram and are such that
$$0 \leqslant d_A \leqslant 0.3, \quad 0.1 \leqslant d_B \leqslant 0.9, \quad 0 \leqslant d_C \leqslant 0.3.$$

\begin{enumerate}[label=(\alph*)]
\item Given that $T_1$ and $T_2$ represent the tension in wires 1 and 2 respectively, show that
$$T_1 = mg(2 + d_A - d_B - d_C),$$
and find a similar expression for $T_2$. [6]

\item \begin{enumerate}[label=(\roman*)]
\item Find the maximum possible value of $T_1$. 

\item Without carrying out any further calculations, write down the maximum possible value of $T_2$. Give a reason for your answer. [3]
\end{enumerate}
\end{enumerate}

\hfill \mbox{\textit{WJEC Unit 4 2019 Q9 [9]}}