| Exam Board | CAIE |
|---|---|
| Module | Further Paper 3 (Further Paper 3) |
| Year | 2021 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Smooth ring on rotating string |
| Difficulty | Moderate -0.5 This is part (b) of a multi-part circular motion question asking for a distance calculation in terms of a given parameter. With only 3 marks and being a middle part of a structured question, it likely involves straightforward application of circular motion principles (resolving forces, using geometry) rather than complex problem-solving. While Further Maths content is inherently harder, this appears to be a routine calculation within that context. |
| Spec | 6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| 3(a) | For B: T =mg | B1 |
| For A: R+Tcosθ=3mg | M1 | All 3 terms, allow sign errors, allow sin/cos mix. |
| Answer | Marks |
|---|---|
| 5 | A1 |
| Answer | Marks |
|---|---|
| 3(b) | 3mv2 |
| Answer | Marks | Guidance |
|---|---|---|
| r | M1 | May be seen in part (a), allow sin/cos mix. |
| r= ARsinθ | B1 | Or equivalent. |
| Answer | Marks |
|---|---|
| 4 4 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 3:
--- 3(a) ---
3(a) | For B: T =mg | B1 | May be embedded.
For A: R+Tcosθ=3mg | M1 | All 3 terms, allow sign errors, allow sin/cos mix.
3
Use given R to obtain cosθ=
5 | A1
3
--- 3(b) ---
3(b) | 3mv2
Tsinθ=
r | M1 | May be seen in part (a), allow sin/cos mix.
r= ARsinθ | B1 | Or equivalent.
3a 1
[Combine to give AR= , so] BR= a
4 4 | A1
3
Question | Answer | Marks | Guidance\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find, in terms of $a$, the distance of $B$ below the ring. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE Further Paper 3 2021 Q3 [3]}}