1 A particle \(P\) of mass 0.3 kg moves in a circle with centre \(O\) on a smooth horizontal surface. \(P\) is attached to \(O\) by a light elastic string of modulus of elasticity 12 N and natural length \(l \mathrm {~m}\). The speed of \(P\) is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and the radius of the circle in which it moves is \(2 l \mathrm {~m}\). Calculate \(l\).

## Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $T = 12$ N | B1 | $T = 12(2L-L)/L$ |
| $T = 0.3 \times 4^2/r$ | M1 | $\text{Accn} = v^2/r$ |
| $12 = 4.8/(2L)$ | A1$\checkmark$ | ft candidates expression for T |
| $L = 0.2$ | A1 | Total: 4 marks |

---

1 A particle $P$ of mass 0.3 kg moves in a circle with centre $O$ on a smooth horizontal surface. $P$ is attached to $O$ by a light elastic string of modulus of elasticity 12 N and natural length $l \mathrm {~m}$. The speed of $P$ is $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, and the radius of the circle in which it moves is $2 l \mathrm {~m}$. Calculate $l$.

\hfill \mbox{\textit{CAIE M2 2016 Q1 [4]}}