AQA M2 2006 January — Question 4 10 marks

Exam BoardAQA
ModuleM2 (Mechanics 2)
Year2006
SessionJanuary
Marks10
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCentre of Mass 1
TypeL-shaped or composite rectangular lamina
DifficultyStandard +0.3 This is a standard M2 centre of mass question involving a composite lamina with symmetry. Part (a) uses symmetry (routine), part (b) requires dividing into rectangles and applying the standard formula (textbook exercise), part (c) uses basic trigonometry with the centre of mass, and part (d) tests conceptual understanding. All techniques are standard for M2 with no novel problem-solving required, making it slightly easier than average.
Spec6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces

4 The diagram shows a uniform lamina \(A B C D E F G H\). \includegraphics[max width=\textwidth, alt={}, center]{6a49fdd7-f180-451c-8f37-ad764fe13dfd-3_346_933_1123_577}
  1. Explain why the centre of mass is 25 cm from \(A H\).
  2. Show that the centre of mass is 4.375 cm from \(H G\).
  3. The lamina is freely suspended from \(A\). Find the angle between \(A B\) and the vertical when the lamina is in equilibrium.
  4. Explain, briefly, how you have used the fact that the lamina is uniform.

4 The diagram shows a uniform lamina $A B C D E F G H$.\\
\includegraphics[max width=\textwidth, alt={}, center]{6a49fdd7-f180-451c-8f37-ad764fe13dfd-3_346_933_1123_577}
\begin{enumerate}[label=(\alph*)]
\item Explain why the centre of mass is 25 cm from $A H$.
\item Show that the centre of mass is 4.375 cm from $H G$.
\item The lamina is freely suspended from $A$. Find the angle between $A B$ and the vertical when the lamina is in equilibrium.
\item Explain, briefly, how you have used the fact that the lamina is uniform.
\end{enumerate}

\hfill \mbox{\textit{AQA M2 2006 Q4 [10]}}