6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a2738ce4-4dc5-4cd1-ac3d-0c3fcf21ea71-09_600_968_292_486}
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\caption{Figure 3}
\end{figure}
Figure 3 shows a rectangular lamina \(O A B C\). The coordinates of \(O , A , B\) and \(C\) are ( 0,0 ), \(( 8,0 ) , ( 8,5 )\) and \(( 0,5 )\) respectively. Particles of mass \(k m , 5 m\) and \(3 m\) are attached to the lamina at \(A , B\) and \(C\) respectively.
The \(x\)-coordinate of the centre of mass of the three particles without the lamina is 6.4.
- Show that \(k = 7\).
The lamina \(O A B C\) is uniform and has mass \(12 m\).
- Find the coordinates of the centre of mass of the combined system consisting of the three particles and the lamina.
The combined system is freely suspended from \(O\) and hangs at rest.
- Find the angle between \(O C\) and the horizontal.