2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9126ebb1-eaa7-4a40-953f-5dc819c9f479-3_631_581_744_769}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{figure}
A uniform ladder \(A B\) has one end \(A\) on smooth horizontal ground. The other end \(B\) rests against a smooth vertical wall. The ladder is modelled as a uniform rod of mass \(m\) and length 4a. The ladder is kept in equilibrium by a horizontal force \(F\) acting at a point \(C\) of the ladder where \(A C = a\). The force \(F\) and the ladder lie in a vertical plane perpendicular to the wall. The ladder is inclined to the horizontal at an angle \(\theta\), where \(\tan \theta = 2\), as shown in Fig. 1.
Find \(F\) in terms of \(m\) and \(g\).
(6 marks)