5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5ef8231d-5b95-4bbb-a8e2-788c708fa078-16_632_734_248_605}
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\caption{Figure 2}
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The uniform lamina \(A B C\) is in the shape of an equilateral triangle with sides of length \(4 a\). The midpoint of \(B C\) is \(D\). The point \(E\) lies on \(A D\) with \(D E = \frac { 3 a } { 2 }\). A circular hole, with centre \(E\) and radius \(a\), is made in the lamina \(A B C\) to form the lamina \(L\), shown shaded in Figure 2.
- Find the distance of the centre of mass of \(L\) from \(D\).
The lamina \(L\) is freely suspended from the point \(B\) and hangs in equilibrium.
- Find, to the nearest degree, the size of the acute angle between \(A D\) and the downward vertical.