| Exam Board | CAIE |
|---|---|
| Module | Further Paper 3 (Further Paper 3) |
| Year | 2021 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | String through hole – lower particle also moves in horizontal circle (conical pendulum below) |
| Difficulty | Challenging +1.2 This is a standard circular motion problem with connected particles requiring force resolution and equilibrium conditions. Part (a) involves straightforward vertical equilibrium (tension balance), while part (b) requires horizontal circular motion equation with centripetal force. The geometry is given clearly, and the methods are direct applications of standard techniques without requiring novel insight or complex multi-step reasoning. |
| Spec | 3.03k Connected particles: pulleys and equilibrium6.05a Angular velocity: definitions |
| Answer | Marks | Guidance |
|---|---|---|
| 3(a) | T =3mg and Tcosθ=mg | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | A1 | At least one step of working, AG. |
| Answer | Marks |
|---|---|
| 3(b) | a−x |
| Answer | Marks | Guidance |
|---|---|---|
| 4 4 2 | B1 | 8 |
| Answer | Marks |
|---|---|
| r | M1 |
| Combining to find an equation in v2, a and g only. | DM1 |
| v2 =2ga, v= 2ga | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 3:
--- 3(a) ---
3(a) | T =3mg and Tcosθ=mg | M1 | Must see both of these separately.
1
Combining, cosθ=
3 | A1 | At least one step of working, AG.
2
--- 3(b) ---
3(b) | a−x
(cosθ= ,where x = AR)
x
3 1 a
AR= a or BR= a or radius =
4 4 2 | B1 | 8
sinθ=
3
mv2
Tsinθ=
r | M1
Combining to find an equation in v2, a and g only. | DM1
v2 =2ga, v= 2ga | A1
4
Question | Answer | Marks | Guidance\includegraphics{figure_3}
Particles $A$ and $B$, of masses $m$ and $3m$ respectively, are connected by a light inextensible string of length $a$ that passes through a fixed smooth ring $R$. Particle $B$ hangs in equilibrium vertically below the ring. Particle $A$ moves in horizontal circles with speed $v$. Particles $A$ and $B$ are at the same horizontal level. The angle between $AR$ and $BR$ is $\theta$ (see diagram).
\begin{enumerate}[label=(\alph*)]
\item Show that $\cos\theta = \frac{1}{3}$. [2]
\item Find an expression for $v$ in terms of $a$ and $g$. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE Further Paper 3 2021 Q3 [6]}}