2.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{9126ebb1-eaa7-4a40-953f-5dc819c9f479-3_631_581_744_769}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\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)\\

\hfill \mbox{\textit{Edexcel M2  Q2 [6]}}