3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{54112b4a-3727-4e5b-97e5-4291e7172438-06_479_608_246_667}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The uniform lamina \(O A B C D\) is shown in Figure 1, with \(O A = 6 a , A B = 3 a , C D = 2 a\) and \(D O = 6 a\) and with right angles at \(O , A\) and \(D\).
- Find the distance of the centre of mass of the lamina
- from \(O D\),
- from \(O A\).
The lamina is suspended from \(C\) and hangs freely in equilibrium with \(C B\) inclined at an angle \(\alpha\) to the vertical.
- Find, to the nearest degree, the size of the angle \(\alpha\).