4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{25c503ad-94c7-4137-83b5-c3e0aea62f0c-07_887_707_269_621}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The uniform plane lamina \(A B C D E F\) shown in Figure 1 is made from two identical rhombuses. Each rhombus has sides of length \(a\) and angle \(B A D =\) angle \(D A F = \theta\). The centre of mass of the lamina is \(0.9 a\) from \(A\).
- Show that \(\cos \theta = 0.8\)
The weight of the lamina is \(W\). A particle of weight \(k W\) is fixed to the lamina at the point \(A\). The lamina is freely suspended from \(B\) and hangs in equilibrium with \(D A\) horizontal.
- Find the value of \(k\).