5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{dadd5bac-b547-42dd-838e-60a786555472-3_303_1301_1089_390}
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\caption{Figure 1}
\end{figure}
A pendulum \(P\) is modelled as a uniform rod \(A B\), of length \(9 a\) and mass \(m\), rigidly fixed to a uniform circular disc of radius \(a\) and mass \(2 m\). The end \(B\) of the rod is attached to the centre of the disc, and the rod lies in the plane of the disc, as shown in Figure 1. The pendulum is free to rotate in a vertical plane about a fixed smooth horizontal axis \(L\) which passes through the end \(A\) and is perpendicular to the plane of the disc.
- Show that the moment of inertia of \(P\) about \(L\) is \(190 m a ^ { 2 }\).
The pendulum makes small oscillations about \(L\).
- By writing down an equation of motion for \(P\), find the approximate period of these small oscillations.