Edexcel M2 2008 January — Question 4

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2008
SessionJanuary
TopicCentre of Mass 1

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f7a2bf93-a7fc-43c5-b317-109320f633ba-05_783_1231_237_358} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A set square \(S\) is made by removing a circle of centre \(O\) and radius 3 cm from a triangular piece of wood. The piece of wood is modelled as a uniform triangular lamina \(A B C\), with \(\angle A B C = 90 ^ { \circ } , A B = 12 \mathrm {~cm}\) and \(B C = 21 \mathrm {~cm}\). The point \(O\) is 5 cm from \(A B\) and 5 cm from \(B C\), as shown in Figure 1.
  1. Find the distance of the centre of mass of \(S\) from
    1. \(A B\),
    2. \(B C\). The set square is freely suspended from \(C\) and hangs in equilibrium.
  2. Find, to the nearest degree, the angle between \(C B\) and the vertical.