4.
\begin{figure}[h]
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\caption{Figure 1}
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The uniform lamina \(O B C\) is one quarter of a circular disc with centre \(O\) and radius 4 m . The points \(A\) and \(D\), on \(O B\) and \(O C\) respectively, are 3 m from \(O\). The uniform lamina \(A B C D\), shown shaded in Figure 1, is formed by removing the triangle \(O A D\) from \(O B C\).
Given that the centre of mass of one quarter of a uniform circular disc of radius \(r\) is at a distance \(\frac { 4 \sqrt { 2 } } { 3 \pi } r\) from the centre of the disc,
- find the distance of the centre of mass of the lamina \(A B C D\) from \(A D\).
The lamina is freely suspended from \(D\) and hangs in equilibrium.
- Find, to the nearest degree, the angle between \(D C\) and the downward vertical.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{deb9e495-3bfb-4a46-9ee7-3eb421c33499-09_915_1269_118_356}
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\caption{Figure 2}
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