5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{cf960066-46b8-42a3-8a8b-d8deb76e7c70-09_522_997_276_477}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\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 \(A B\).
- Show that \(F = \frac { 3 a m g \cos \theta } { b }\).
- Find, in terms of \(a , b , g , m\) and \(\theta\),
- the horizontal component of the force acting on the rod at \(A\),
- 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,
- find the value of \(\frac { a } { b }\).