Edexcel M2 2011 June — Question 4

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2011
SessionJune
TopicCentre of Mass 1

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e8329378-c976-4068-95ff-e2d254546d6d-05_394_846_239_555} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a uniform lamina \(A B C D E\) such that \(A B D E\) is a rectangle, \(B C = C D\), \(A B = 4 a\) and \(A E = 2 a\). The point \(F\) is the midpoint of \(B D\) and \(F C = a\).
  1. Find, in terms of \(a\), the distance of the centre of mass of the lamina from \(A E\). The lamina is freely suspended from \(A\) and hangs in equilibrium.
  2. Find the angle between \(A B\) and the downward vertical.