| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Particle attached to lamina - find mass/position |
| Difficulty | Standard +0.3 This is a standard M2 centre of mass question involving composite shapes and equilibrium. Part (a) requires routine calculation using symmetry and the formula for composite bodies (6 marks shown). Part (b) involves taking moments about the suspension point with the added particle, which is a textbook application. The geometry is straightforward and the methods are well-practiced in M2, making this slightly easier than average overall. |
| Spec | 6.04b Find centre of mass: using symmetry6.04d Integration: for centre of mass of laminas/solids6.04e Rigid body equilibrium: coplanar forces |
2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{1822f86a-9089-44af-ab36-6006adfeb5b9-03_709_620_116_667}
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\caption{Figure 1}
\end{center}
\end{figure}
The uniform lamina $O A B C D$, shown in Figure 1, is formed by removing the triangle $O A D$ from the square $A B C D$ with centre $O$. The square has sides of length $2 a$.
\begin{enumerate}[label=(\alph*)]
\item Show that the centre of mass of $O A B C D$ is $\frac { 2 } { 9 } a$ from $O$.
The mass of the lamina is $M$. A particle of mass $k M$ is attached to the lamina at $D$ to form the system $S$. The system $S$ is freely suspended from $A$ and hangs in equilibrium with $A O$ vertical.
\item Find the value of $k$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2015 Q2 [8]}}