5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e6d100ff-dd4a-4591-a0a3-81761773045e-09_689_581_237_683}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The uniform lamina \(A B C D E F\), shown in Figure 2, consists of two identical rectangles with sides of length \(a\) and \(3 a\). The mass of the lamina is \(M\). A particle of mass \(k M\) is attached to the lamina at \(E\). The lamina, with the attached particle, is freely suspended from \(A\) and hangs in equilibrium with \(A F\) at an angle \(\theta\) to the downward vertical.
Given that \(\tan \theta = \frac { 4 } { 7 }\), find the value of \(k\).
(10)