| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2021 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 2 |
| Type | Centre of mass of solid of revolution |
| Difficulty | Standard +0.8 This is a standard M3/Further Mechanics centre of mass question requiring volume and centroid calculations for a solid of revolution. While it involves multiple integration steps and algebraic manipulation (finding limits, setting up integrals with y², then y⁴ terms), the techniques are routine for Further Maths students. The 'show that' in part (a) provides a check, and the method is direct application of standard formulas without requiring novel insight. |
| Spec | 4.08d Volumes of revolution: about x and y axes6.04d Integration: for centre of mass of laminas/solids |
\begin{enumerate}
\item The finite region enclosed by the curve with equation $y = 3 - \sqrt { x }$ and the lines $x = 0$ and $y = 0$ is rotated through $2 \pi$ radians about the $x$-axis, to form a uniform solid $S$.
\end{enumerate}
Use algebraic integration to\\
(a) show that the volume of $S$ is $\frac { 27 } { 2 } \pi$\\
(b) find the $x$ coordinate of the centre of mass of $S$.
\hfill \mbox{\textit{Edexcel M3 2021 Q3 [9]}}