| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | L-shaped or composite rectangular lamina |
| Difficulty | Standard +0.3 This is a standard M2 centre of mass question involving composite shapes with straightforward rectangular components. Part (a) requires understanding symmetry (routine concept), part (b) involves standard moment calculations with clearly defined dimensions, and part (c) applies the equilibrium condition for a suspended lamina using basic trigonometry. All techniques are textbook-standard 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 |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Part (a): Symmetry of the lamina about \(PQ\) | E1 | Accept 'mirror line' |
| Part (b): Taking moments about \(AB\): \(600\rho \times 15 + 100\rho \times 35 = 700\rho\bar{x}\); \(\bar{x} = 17.857 = 17.9\) cm | M1A1, A1, A1 | Condone lack of \(\rho\); SC3 17.8 |
| Part (c): \(\tan\theta = \frac{10}{17.857} = 0.56\); Angle is 29.2488... = 29° | M1A1, M1, A1 | M1 for use of \(\tan\theta\) |
| Total: 9 |
| Answer/Working | Marks | Guidance |
|---|---|---|
| **Part (a):** Symmetry of the lamina about $PQ$ | E1 | Accept 'mirror line' |
| **Part (b):** Taking moments about $AB$: $600\rho \times 15 + 100\rho \times 35 = 700\rho\bar{x}$; $\bar{x} = 17.857 = 17.9$ cm | M1A1, A1, A1 | Condone lack of $\rho$; SC3 17.8 |
| **Part (c):** $\tan\theta = \frac{10}{17.857} = 0.56$; Angle is 29.2488... = 29° | M1A1, M1, A1 | M1 for use of $\tan\theta$ |
| | | **Total: 9** |2 A uniform lamina is in the shape of a rectangle $A B C D$ and a square $E F G H$, as shown in the diagram.
The length $A B$ is 20 cm , the length $B C$ is 30 cm , the length $D E$ is 5 cm and the length $E F$ is 10 cm .
The point $P$ is the midpoint of $A B$ and the point $Q$ is the midpoint of $H G$.\\
\includegraphics[max width=\textwidth, alt={}, center]{676e753d-1b80-413c-a4b9-21861db8dde5-2_615_1221_1585_429}
\begin{enumerate}[label=(\alph*)]
\item Explain why the centre of mass of the lamina lies on $P Q$.
\item Find the distance of the centre of mass of the lamina from $A B$.
\item The lamina is freely suspended from $A$.
Find, to the nearest degree, the angle between $A D$ and the vertical when the lamina is in equilibrium.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2007 Q2 [9]}}