| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Lamina with removed triangle/rectangle/square |
| Difficulty | Standard +0.8 This is a multi-part centre of mass problem requiring coordinate setup, calculation of areas and centroids for composite shapes (triangle minus square), then a second calculation with an added particle. Part (a) involves 7 marks of algebraic manipulation with multiple geometric relationships. Part (b) requires understanding how adding mass shifts the centre of mass. While the techniques are standard M2 content, the geometric complexity, multi-step nature, and algebraic demands make this moderately harder than average. |
| Spec | 6.04c Composite bodies: centre of mass6.04d Integration: for centre of mass of laminas/solids |
\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 midpoint 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 $NG = \frac{8}{7}a$.
[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 Q4 [11]}}