| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 2 |
| Type | Conical pendulum (horizontal circle) |
| Difficulty | Moderate -0.8 This is a standard conical pendulum problem requiring straightforward application of circular motion principles. Part (i) involves resolving forces vertically (T cos θ = mg) with given geometry, while part (ii) uses horizontal resolution (T sin θ = mv²/r). The geometry is provided explicitly (0.5m string, 0.4m vertical drop gives sin θ = 0.6), making this a routine two-step exercise with no problem-solving insight required—easier than average A-level mechanics. |
| Spec | 3.03b Newton's first law: equilibrium3.03e Resolve forces: two dimensions6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(T\cos\theta = 0.2g\), \(T \times \frac{0.4}{0.5} = 2\) | M1 | Weight = vertical comp of tension |
| \(T = 2.5\) N (AG) | A1 | |
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(2.5\sin\theta = \frac{0.2v^2}{r}\) | M1 | Horiz comp of tension and \(\text{accn} = v^2/r\) |
| \(2.5 \times \frac{0.3}{0.5} = \frac{0.2v^2}{0.3}\) | A1 | |
| \(v = 1.5 \text{ ms}^{-1}\) | A1 | |
| Total: 3 |
## Question 2(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $T\cos\theta = 0.2g$, $T \times \frac{0.4}{0.5} = 2$ | M1 | Weight = vertical comp of tension |
| $T = 2.5$ N (AG) | A1 | |
| **Total: 2** | | |
---
## Question 2(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $2.5\sin\theta = \frac{0.2v^2}{r}$ | M1 | Horiz comp of tension and $\text{accn} = v^2/r$ |
| $2.5 \times \frac{0.3}{0.5} = \frac{0.2v^2}{0.3}$ | A1 | |
| $v = 1.5 \text{ ms}^{-1}$ | A1 | |
| **Total: 3** | | |
---2 One end of a light inextensible string of length 0.5 m is attached to a fixed point $A$. A particle $P$ of mass 0.2 kg is attached to the other end of the string. $P$ moves with constant speed in a horizontal circle with centre $O$ which is 0.4 m vertically below $A$.\\
(i) Show that the tension in the string is 2.5 N .\\
(ii) Find the speed of $P$.\\
\hfill \mbox{\textit{CAIE M2 Q2 [5]}}