| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2015 |
| Session | June |
| Marks | 10 |
| 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 centre of mass question requiring volume and moment calculations using Pappus's theorem formulas. While it involves multiple integration steps with exponential functions and careful algebraic manipulation, the method is routine for students who have practiced solids of revolution. The 'show that' in part (a) provides a target to verify, and part (b) follows the standard formula. Slightly above average difficulty due to the exponential function and algebraic complexity, but not requiring novel insight. |
| Spec | 4.08d Volumes of revolution: about x and y axes6.04d Integration: for centre of mass of laminas/solids |
2. The finite region bounded by the $x$-axis, the curve with equation $y = 2 \mathrm { e } ^ { x }$, the $y$-axis and the line $x = 1$ is rotated through one complete revolution about the $x$-axis to form a uniform solid.
Use algebraic integration to
\begin{enumerate}[label=(\alph*)]
\item show that the volume of the solid is $2 \pi \left( \mathrm { e } ^ { 2 } - 1 \right)$,
\item find, in terms of e, the $x$ coordinate of the centre of mass of the solid.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2015 Q2 [10]}}