| Exam Board | OCR |
|---|---|
| Module | FM1 AS (Further Mechanics 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 10 |
| Topic | Circular Motion 1 |
| Type | String through hole – lower particle also moves in horizontal circle (conical pendulum below) |
| Difficulty | Standard +0.8 This is a Further Maths FM1 question involving coupled circular motion with both horizontal and conical components. It requires setting up equations for two connected particles in different planes, applying Newton's second law in circular motion, resolving forces in multiple directions, and using trigonometry. While the individual techniques are standard, the 3D geometry and coupling of two circular motions makes this more challenging than typical A-level mechanics questions. |
| Spec | 6.05b Circular motion: v=r*omega and a=v^2/r |
3\\
Two particles $A$ and $B$ are connected by a light inextensible string. Particle $A$ has mass 1.2 kg and moves on a smooth horizontal table in a circular path of radius 0.6 m and centre $O$. The string passes through a small smooth hole at $O$. Particle $B$ moves in a horizontal circle in such a way that it is always vertically below $A$. The angle that the portion of the string below the table makes with the downwards vertical through $O$ is $\theta$, where $\cos \theta = \frac { 4 } { 5 }$ (see diagram).\\
\includegraphics[max width=\textwidth, alt={}, center]{75f629e7-969d-43ae-8222-031875ae54ae-02_453_696_1571_552}
\begin{enumerate}[label=(\alph*)]
\item Find the time taken for the particles to perform a complete revolution.
\item Find the mass of $B$.
\end{enumerate}
\hfill \mbox{\textit{OCR FM1 AS 2021 Q3 [10]}}