| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2001 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Solid with removed cone from cone or cylinder |
| Difficulty | Standard +0.3 This is a standard M3 centre of mass question using the composite body formula with straightforward geometry. Part (a) requires routine application of the centre of mass formula for composite bodies (cylinder minus cone), while part (b) involves basic equilibrium with moments about the suspension point. The calculations are methodical but not conceptually demanding, making it slightly easier than average for M3 level. |
| Spec | 6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces |
\includegraphics{figure_3}
An ornament $S$ is formed by removing a solid right circular cone, of radius $r$ and height $\frac{1}{2}h$, from a solid uniform cylinder, of radius $r$ and height $h$, as shown in Fig. 3.
\begin{enumerate}[label=(\alph*)]
\item Show that the distance of the centre of mass $S$ from its plane face is $\frac{19}{30}h$. [7]
\end{enumerate}
The ornament is suspended from a point on the circular rim of its open end. It hangs in equilibrium with its axis of symmetry inclined at an angle $\alpha$ to the horizontal. Given that $h = 4r$,
\begin{enumerate}[label=(\alph*)]\setcounter{enumi}{1}
\item find, in degrees to one decimal place, the value of $\alpha$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2001 Q5 [11]}}