4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e8329378-c976-4068-95ff-e2d254546d6d-05_394_846_239_555}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a uniform lamina \(A B C D E\) such that \(A B D E\) is a rectangle, \(B C = C D\), \(A B = 4 a\) and \(A E = 2 a\). The point \(F\) is the midpoint of \(B D\) and \(F C = a\).
- Find, in terms of \(a\), the distance of the centre of mass of the lamina from \(A E\).
The lamina is freely suspended from \(A\) and hangs in equilibrium.
- Find the angle between \(A B\) and the downward vertical.