5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2656d4b4-7f47-48db-9d7e-07db6ecb8606-6_501_696_316_726}
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\caption{Figure 2}
\end{figure}
The uniform L-shaped lamina \(O A B C D E\), shown in Figure 2, is made from two identical rectangles. Each rectangle is 4 metres long and \(a\) metres wide. Giving each answer in terms of \(a\), find the distance of the centre of mass of the lamina from
- \(O E\),
- \(O A\).
The lamina is freely suspended from \(O\) and hangs in equilibrium with \(O E\) at an angle \(\theta\) to the downward vertical through \(O\), where \(\tan \theta = \frac { 4 } { 3 }\).
- Find the value of \(a\).