| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2002 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Lamina with removed triangle/rectangle/square |
| Difficulty | Standard +0.3 This is a standard M2 centre of mass question requiring systematic application of the composite body formula. Part (a) involves finding centres of mass of triangle and square, then using the removal formula—routine but multi-step. Part (b) applies the particle attachment formula. While requiring careful coordinate work and algebra across 11 marks, it follows predictable M2 patterns without requiring novel insight or particularly challenging problem-solving. |
| Spec | 6.04c Composite bodies: centre of mass6.04d Integration: for centre of mass of laminas/solids |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working: \(\overline{x} = \frac{30}{41}a\) | B1, B1, M1, B1, CSO | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working: \(K = \frac{2}{25}\) or \(K = \frac{3}{25}\) or grant 0.055 | M1, A2(1,0) | A1 |
## (a)
**Answer/Working:** $\overline{x} = \frac{30}{41}a$ | B1, B1, M1, B1, CSO | A1 | 7
## (b)
**Answer/Working:** $K = \frac{2}{25}$ or $K = \frac{3}{25}$ or grant 0.055 | M1, A2(1,0) | A1 | $\frac{4}{15}$
---\includegraphics{figure_1}
Figure 1 shows a template made by removing a square $WXYZ$ from a uniform triangular lamina $ABC$. The lamina is isosceles with $CA = CB$ and $AB = 12a$. The mid-point of $AB$ is $N$ and $NC = 8a$. The centre $O$ of the square lies on $NC$ and $ON = 2a$. The sides $WX$ and $ZY$ are parallel to $AB$ and $WZ = 2a$. The centre of mass of the template is at $G$.
\begin{enumerate}[label=(\alph*)]
\item Show that $NG = \frac{30}{11}a$.
[7]
\end{enumerate}
The template has mass $M$. A small metal stud of mass $kM$ is attached to the template at $C$. The centre of mass of the combined template and stud lies on $YZ$. By modelling the stud as a particle,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item calculate the value of $k$.
[4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2002 Q4 [11]}}