June 2022 Paper 2 Q14
14 A £2 coin has a diameter of 28 mm and a mass of 12 grams.
A uniform rod \(AB\) of length 160 mm and a fixed load of mass \(m\) grams are used to check that a £2 coin has the correct mass.
The rod rests with its midpoint on a support.
A £2 coin is placed face down on the rod with part of its curved edge directly above \(A\).
The fixed load is hung by a light inextensible string from a point directly below the other end of the rod at \(B\), as shown in the diagram.
(a) Given that the rod is horizontal and rests in equilibrium, find \(m\). [3 marks]
(b) State an assumption you have made about the £2 coin to answer part (a). [1 mark]
| Scheme | Marks | AO |
|---|---|---|
| Forms a dimensionally correct non-zero moment For example \(0.012g \times 0.066\) \(0.012g \times 66\) \(12g \times 66\) \(160mg\) | B1 | 3.3 |
| Obtains a correct single equation where the only unknown is the mass This might come from correct moments about a point other than the centre with forces correctly resolved in the vertical direction, but these equations must be combined to eliminate the force at the centre PI by 9.9 | M1 | 1.1a |
| Obtains 9.9 Condone \(m\) = 0.0099 kg OE provided units are included if \(m\) is not in grams | A1 | 1.1b |
| (3) |
Typical solution
\[66 \times 12g = 80mg\]\[m = 9.9\]| Scheme | Marks | AO |
|---|---|---|
| States a valid assumption about the £2 coin with no contradictions or incorrect statements For example Models the coin as uniform, or weight acts through the centre or centre of mass is at the centre Do not accept ‘mass acts’ or ‘centre of mass acts’ at the centre or ‘centre of weight’ or ‘weight is at’ | E1 | 3.5a |
| (1) | ||
| (4 marks) |
Typical solution
The coin is uniform