| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2014 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 2 |
| Type | Centre of mass of lamina by integration |
| Difficulty | Standard +0.8 This is a centre of mass problem requiring integration of a triangular lamina with non-trivial geometry. Students must set up the correct integral with variable strip width (y as a function of x for an equilateral triangle), apply the centre of mass formula, and handle the algebraic manipulation. While the symmetry simplifies finding ȳ, finding x̄ requires careful setup and integration, making this moderately challenging but within standard M3 scope. |
| Spec | 6.04d Integration: for centre of mass of laminas/solids |
2.
\begin{figure}[h]
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\caption{Figure 1}
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A uniform lamina $L$ is in the shape of an equilateral triangle of side $2 a$. The lamina is placed in the $x y$-plane with one vertex at the origin $O$ and an axis of symmetry along the $x$-axis, as shown in Figure 1.
Use algebraic integration to find the $x$ coordinate of the centre of mass of $L$.\\
\hfill \mbox{\textit{Edexcel M3 2014 Q2 [6]}}