3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{64b0abc9-4021-44e6-8bf7-1a5862617085-08_744_369_246_447}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{64b0abc9-4021-44e6-8bf7-1a5862617085-08_538_593_452_1023}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The uniform rectangular lamina \(A B D E\), shown in Figure 1, has side \(A B\) of length \(2 a\) and side \(B D\) of length \(6 a\). The point \(C\) divides \(B D\) in the ratio 1:2 and the point \(F\) divides \(E A\) in the ratio \(1 : 2\). The rectangular lamina is folded along \(F C\) to produce the folded lamina \(L\), shown in Figure 2.
- Show that the centre of mass of \(L\) is \(\frac { 16 } { 9 } a\) from \(E F\).
The folded lamina, \(L\), is freely suspended from \(C\) and hangs in equilibrium.
- Find the size of the angle between \(C F\) and the downward vertical.