| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2010 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Lamina with attached triangle |
| Difficulty | Moderate -0.3 This is a straightforward centre of mass problem requiring standard application of the formula with two components. Part (a) is a simple symmetry argument, and part (b) involves routine calculation using moments about a point. The setup is clear, the masses and positions are given explicitly, and no novel problem-solving insight is required—just methodical application of a standard technique. |
| Spec | 6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Both laminas are uniform and symmetric about line \(AB\) | B1 | Must reference symmetry about \(AB\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Taking moments about \(B\): \((0.4 + 0.1)\bar{x} = 0.4 \times 4 + 0.1 \times (4+2)\) | M1 | Moments equation with correct distances |
| \(0.5\bar{x} = 1.6 + 0.6 = 2.2\) | A1 | |
| \(\bar{x} = 4.4\) cm from \(B\) | A1 |
## Question 3:
**(a)**
| Answer | Mark | Guidance |
|--------|------|----------|
| Both laminas are uniform and symmetric about line $AB$ | B1 | Must reference symmetry about $AB$ |
**(b)**
| Answer | Mark | Guidance |
|--------|------|----------|
| Taking moments about $B$: $(0.4 + 0.1)\bar{x} = 0.4 \times 4 + 0.1 \times (4+2)$ | M1 | Moments equation with correct distances |
| $0.5\bar{x} = 1.6 + 0.6 = 2.2$ | A1 | |
| $\bar{x} = 4.4$ cm from $B$ | A1 | |3 A uniform circular lamina, of radius 4 cm and mass 0.4 kg , has a centre $O$, and $A B$ is a diameter. To create a medal, a smaller uniform circular lamina, of radius 2 cm and mass 0.1 kg , is attached so that the centre of the smaller lamina is at the point $A$, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{3ffa0a2b-aa7d-46eb-b92b-3e3ee59f235c-06_671_878_513_598}
\begin{enumerate}[label=(\alph*)]
\item Explain why the centre of mass of the medal is on the line $A B$.
\item Find the distance of the centre of mass of the medal from the point $B$.\\
\includegraphics[max width=\textwidth, alt={}, center]{3ffa0a2b-aa7d-46eb-b92b-3e3ee59f235c-06_1259_1705_1448_155}
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{3ffa0a2b-aa7d-46eb-b92b-3e3ee59f235c-07_2484_1709_223_153}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2010 Q3 [4]}}