Edexcel M2 2014 June — Question 3

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2014
SessionJune
TopicCentre of Mass 1

3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{47420c50-c232-41e9-8c4d-a890d86ea933-04_814_1127_219_411} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} The uniform lamina \(A B C D E F\), shown shaded in Figure 1, is symmetrical about the line through \(B\) and \(E\). It is formed by removing the isosceles triangle \(F E D\), of height \(6 a\) and base \(8 a\), from the isosceles triangle \(A B C\) of height \(9 a\) and base \(12 a\).
  1. Find, in terms of \(a\), the distance of the centre of mass of the lamina from \(A C\). The lamina is freely suspended from \(A\) and hangs in equilibrium.
  2. Find, to the nearest degree, the size of the angle between \(A B\) and the downward vertical.