| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Lamina with removed circle/semicircle |
| Difficulty | Standard +0.3 This is a standard M2 centre of mass problem requiring composite body techniques (square minus semicircle) and equilibrium of a suspended lamina. The calculations are straightforward: find centroids using standard formulas, apply the composite body formula, then use the equilibrium condition that the centre of mass hangs directly below the point of suspension. While it requires multiple steps and careful bookkeeping, it follows a well-practiced procedure with no novel insight needed, making it slightly easier than average. |
| Spec | 6.03e Impulse: by a force6.03f Impulse-momentum: relation6.04d Integration: for centre of mass of laminas/solids6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks |
|---|---|
| 4 | m |
Question 4:
4 | m
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© OCR 2013 4729/01 Jan13\includegraphics{figure_4}
A uniform square lamina $ABCD$ of side 6 cm has a semicircular piece, with $AB$ as diameter, removed (see diagram).
\begin{enumerate}[label=(\roman*)]
\item Find the distance of the centre of mass of the remaining shape from $CD$. [6]
\end{enumerate}
The remaining shape is suspended from a fixed point by a string attached at $C$ and hangs in equilibrium.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the angle between $CD$ and the vertical. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR M2 2013 Q4 [8]}}