| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Moments |
| Type | Rod or object resting on curved surface |
| Difficulty | Challenging +1.2 This is a multi-part equilibrium problem requiring understanding of normal reactions on curved surfaces, force diagrams, and taking moments. Part (a) tests conceptual understanding of smooth contact, part (b) is routine diagram drawing, and part (c) requires setting up moment equations with some geometric reasoning about the configuration. The geometry is moderately involved but the problem follows a standard M2 pattern for rigid body equilibrium, making it slightly above average difficulty. |
| Spec | 3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
9 A smooth hollow hemisphere, of radius $a$ and centre $O$, is fixed so that its rim is in a horizontal plane. A smooth uniform $\operatorname { rod } A B$, of mass $m$, is in equilibrium, with one end $A$ resting on the inside of the hemisphere and the point $C$ on the rod being in contact with the rim of the hemisphere. The rod, of length $l$, is inclined at an angle $\theta$ to the horizontal, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{85514b55-3f13-4746-a3ef-747239b64cca-6_453_828_559_591}
\begin{enumerate}[label=(\alph*)]
\item Explain why the reaction between the rod and the hemisphere at point $A$ acts through $O$.
\item Draw a diagram to show the forces acting on the rod.
\item Show that $l = \frac { 4 a \cos 2 \theta } { \cos \theta }$.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2013 Q9 [8]}}