4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5f79f83-ccfb-47a5-8100-88db81fd0862-07_728_748_214_639}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The uniform square lamina \(A B C D\) shown in Figure 2 has sides of length 4a. The points \(E\) and \(F\), on \(D A\) and \(D C\) respectively, are both at a distance \(3 a\) from \(D\).
The portion \(D E F\) of the lamina is folded through \(180 ^ { \circ }\) about \(E F\) to form the folded lamina \(A B C F E\) shown in Figure 3 below.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5f79f83-ccfb-47a5-8100-88db81fd0862-07_709_730_1395_639}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
- Show that the distance from \(A B\) of the centre of mass of the folded lamina is \(\frac { 55 } { 32 } a\).
(6)
The folded lamina is freely suspended from \(E\) and hangs in equilibrium. - Find the size of the angle between \(E D\) and the downward vertical.