4.
\section*{Figure 1}
\includegraphics[max width=\textwidth, alt={}]{a89db1ee-073c-43a3-8480-44970e51c6e2-4_671_781_442_691}
A uniform lamina \(L\) is formed by taking a uniform square sheet of material \(A B C D\), of side 10 cm , and removing the semi-circle with diameter \(A B\) from the square, as shown in Fig. 2.
- Find, in cm to 2 decimal places, the distance of the centre of mass of the lamina \(L\) from the mid-point of \(A B\).
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[The centre of mass of a uniform semi-circular lamina, radius \(a\), is at a distance \(\frac { 4 a } { 3 \pi }\) from the centre of the bounding diameter.]
The lamina is freely suspended from \(D\) and hangs at rest. - Find, in degrees to one decimal place, the angle between CD and the vertical.