5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{99d06f7b-f5cc-4c19-ae26-8f715eda8ee8-16_419_531_214_708}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a uniform rectangular lamina \(A B C D\) with sides of length \(3 a\) and \(k a\), where \(k > 3\). The point \(E\) on side \(A D\) is such that \(D E = 3 a\). Rectangle \(A B C D\) is folded along the line \(C E\) to produce the folded lamina \(L\) shown in Figure 4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{99d06f7b-f5cc-4c19-ae26-8f715eda8ee8-16_455_536_941_703}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Find, in terms of \(a\) and \(k\),
- the distance of the centre of mass of \(L\) from \(A B\),
- the distance of the centre of mass of \(L\) from \(A E\).
The folded lamina \(L\) is freely suspended from \(A\) and hangs in equilibrium with \(A B\) at \(45 ^ { \circ }\) to the downward vertical.
- Find, to 3 significant figures, the value of \(k\).