| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Suspended lamina equilibrium angle |
| Difficulty | Standard +0.3 This is a standard M2 centre of mass question with routine calculations. Part (a) requires basic moment calculations about an axis, part (b) is a symmetry observation requiring minimal work, and part (c) involves straightforward trigonometry (tan θ = horizontal distance / vertical distance) once the centre of mass is known. The question follows a predictable template with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \((10 \times 40)\rho \times 5 + (10 \times 60)\rho \times 40 = (10 \times 40 + 10 \times 60)\rho \bar{y}\) giving \(\bar{y} = 26 \text{ cm}\) | M1, M1, A1, A1 | |
| (b) Symmetry of shape | B1 | |
| (c) \(\tan \theta = \frac{26}{13}\) or inverted, must see 26; \(\theta = 63°\) (63.4) | M1, M1, A1, A1 | Attempting subtraction leading to 13 cm; Or inverted, must see 26 or inverted; Accept \(117°\) |
**(a)** $(10 \times 40)\rho \times 5 + (10 \times 60)\rho \times 40 = (10 \times 40 + 10 \times 60)\rho \bar{y}$ giving $\bar{y} = 26 \text{ cm}$ | M1, M1, A1, A1 | | **Total: 4 marks**
**(b)** Symmetry of shape | B1 | | **Total: 1 mark**
**(c)** $\tan \theta = \frac{26}{13}$ or inverted, must see 26; $\theta = 63°$ (63.4) | M1, M1, A1, A1 | Attempting subtraction leading to 13 cm; Or inverted, must see 26 or inverted; Accept $117°$ | **Total: 4 marks**
**Question 4 Total: 9 marks**
---4 A uniform T-shaped lamina is formed by rigidly joining two rectangles $A B C H$ and $D E F G$, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{480a817d-074f-440d-829e-c8f8a9746151-4_748_652_456_644}
\begin{enumerate}[label=(\alph*)]
\item Show that the centre of mass of the lamina is 26 cm from the edge $A B$.
\item Explain why the centre of mass of the lamina is 5 cm from the edge $G F$.
\item The point $X$ is on the edge $A B$ and is 7 cm from $A$, as shown in the diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{480a817d-074f-440d-829e-c8f8a9746151-4_697_534_1576_753}
The lamina is freely suspended from $X$ and hangs in equilibrium.\\
Find the angle between the edge $A B$ and the vertical, giving your answer to the nearest degree.\\
(4 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2007 Q4 [9]}}