| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2003 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Cone stability and toppling conditions |
| Difficulty | Challenging +1.2 This is a multi-part M3 centre of mass problem requiring composite body calculations and equilibrium analysis. Part (a) involves standard centre of mass formulas for cone and hemisphere, while part (b) requires understanding the toppling condition (centre of mass directly above contact point). The algebra is moderately involved but the concepts are standard M3 material with no novel insight required. |
| Spec | 6.04c Composite bodies: centre of mass6.04d Integration: for centre of mass of laminas/solids |
\begin{enumerate}[label=(\alph*)]
\item Show that the distance $d$ of the centre of mass of the toy from its lowest point $O$ is given by
$$d = \frac { h ^ { 2 } + 2 h r + 5 r ^ { 2 } } { 2 ( h + 4 r ) } .$$
When the toy is placed with any point of the curved surface of the hemisphere resting on the plane it will remain in equilibrium.
\item Find $h$ in terms of $r$.\\
(3)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2003 Q3 [10]}}