| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2012 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Equilibrium with applied force |
| Difficulty | Standard +0.3 This is a straightforward centre of mass problem requiring standard formulas for composite bodies and basic equilibrium. Students must find the combined centre of mass using moments (two calculations with simple arithmetic), then apply vertical equilibrium and moments about a point to find two tensions. All steps are routine M2 techniques with no conceptual challenges or novel problem-solving required. |
| Spec | 6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces |
3 A uniform rectangular lamina $A B C D$, of mass 1.6 kg , has side $A B$ of length 12 cm and side $B C$ of length 8 cm .
To create a logo, a uniform circular lamina, of mass 0.4 kg , is attached. The centre of the circular lamina is at the point $C$, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{088327c1-acd3-486d-b76f-1fe2560ffaff-3_520_780_593_630}
\begin{enumerate}[label=(\alph*)]
\item Find the distance of the centre of mass of the logo:
\begin{enumerate}[label=(\roman*)]
\item from the line $A B$;
\item from the line $A D$.
\end{enumerate}\item The logo is suspended in equilibrium, with $A B$ horizontal, by two vertical strings. One string is attached at the point $A$ and the other string is attached at the point $B$.
Find the tension in each of the two strings.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2012 Q3 [11]}}