| Exam Board | Edexcel |
|---|---|
| Module | FM2 (Further Mechanics 2) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Centre of mass with variable parameter |
| Difficulty | Standard +0.3 This is a straightforward Further Maths mechanics question requiring integration of a linear density function. Part (a) is a 'show that' involving a simple integral, and part (b) requires the standard centre of mass formula. The linear function makes integration routine, and the question follows a standard template with no novel problem-solving required. |
| Spec | 1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08d Evaluate definite integrals: between limits6.04c Composite bodies: centre of mass6.04d Integration: for centre of mass of laminas/solids |
\begin{enumerate}
\item A flag pole is 15 m long.
\end{enumerate}
The flag pole is non-uniform so that, at a distance $x$ metres from its base, the mass per unit length of the flag pole, $m \mathrm {~kg} \mathrm {~m} ^ { - 1 }$ is given by the formula $m = 10 \left( 1 - \frac { x } { 25 } \right)$.
The flag pole is modelled as a rod.\\
(a) Show that the mass of the flag pole is 105 kg .\\
(b) Find the distance of the centre of mass of the flag pole from its base.
\hfill \mbox{\textit{Edexcel FM2 Q1 [7]}}