| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2022 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Moments |
| Type | Rod or block on rough surface in limiting equilibrium (no wall) |
| Difficulty | Challenging +1.2 This is a standard mechanics statics problem requiring moment equilibrium and friction at limiting equilibrium. While it involves multiple forces and careful geometry with the 60° angles, the solution follows a systematic approach: take moments about A to find tension, then resolve forces and apply limiting friction. The algebra is moderately involved but the conceptual framework is routine for M1/M2 level, making it somewhat above average difficulty but not requiring novel insight. |
| Spec | 3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
\includegraphics{figure_11}
A uniform rod $AB$ of mass 4 kg and length 3 m rests in a vertical plane with $A$ on rough horizontal ground.
A particle of mass 1 kg is attached to the rod at $B$. The rod makes an angle of $60°$ with the horizontal and is held in limiting equilibrium by a light inextensible string $CD$. $D$ is a fixed point vertically above $A$ and $CD$ makes an angle of $60°$ with the vertical. The distance $AC$ is $x$ m (see diagram).
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $g$ and $x$, the tension in the string. [3]
\end{enumerate}
The coefficient of friction between the rod and the ground is $\frac{9\sqrt{3}}{35}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the value of $x$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2022 Q11 [7]}}