2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1822f86a-9089-44af-ab36-6006adfeb5b9-03_709_620_116_667}
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\caption{Figure 1}
\end{figure}
The uniform lamina \(O A B C D\), shown in Figure 1, is formed by removing the triangle \(O A D\) from the square \(A B C D\) with centre \(O\). The square has sides of length \(2 a\).
- Show that the centre of mass of \(O A B C D\) is \(\frac { 2 } { 9 } a\) from \(O\).
The mass of the lamina is \(M\). A particle of mass \(k M\) is attached to the lamina at \(D\) to form the system \(S\). The system \(S\) is freely suspended from \(A\) and hangs in equilibrium with \(A O\) vertical.
- Find the value of \(k\).