5.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{cf960066-46b8-42a3-8a8b-d8deb76e7c70-09_522_997_276_477}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

A uniform rod $A B$, of mass $m$ and length $2 a$, is freely hinged to a fixed point $A$. A particle of mass $m$ is attached to the rod at $B$. The rod is held in equilibrium at an angle $\theta$ to the horizontal by a force of magnitude $F$ acting at the point $C$ on the rod, where $A C = b$, as shown in Figure 3. The force at $C$ acts at right angles to $A B$ and in the vertical plane containing $A B$.
\begin{enumerate}[label=(\alph*)]
\item Show that $F = \frac { 3 a m g \cos \theta } { b }$.
\item Find, in terms of $a , b , g , m$ and $\theta$,
\begin{enumerate}[label=(\roman*)]
\item the horizontal component of the force acting on the rod at $A$,
\item the vertical component of the force acting on the rod at $A$.

Given that the force acting on the rod at $A$ acts along the rod,
\end{enumerate}\item find the value of $\frac { a } { b }$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2013 Q5 [13]}}