Edexcel M2 2018 January — Question 3

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2018
SessionJanuary
TopicCentre of Mass 1

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 \(D\).
  1. Find the distance of the centre of mass of the lamina
    1. from \(O D\),
    2. 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.
  2. Find, to the nearest degree, the size of the angle \(\alpha\).