Paper 1 Measurement Answers

1. C - Kelvin is the SI base unit for thermodynamic temperature in the 9749 recall list.
2. B - Pressure is force per area, so $\mathrm{Pa}=\mathrm{N}{\mathrm{m}}^{-2}=\mathrm{kg}{\mathrm{m}}^{-1}{\mathrm{s}}^{-2}$.
3. B - $k=x/t^2$, so its unit is $\mathrm{m}{\mathrm{s}}^{-2}$.
4. D - $m{v}^2$ has unit of energy, while radius $r$ has unit of length; the equation adds incompatible terms.
5. A - $1\mathrm{mm}=10^{-3}\mathrm{m}$, so $0.48\mathrm{mm}=4.8\times 10^{-4}\mathrm{m}$.
6. C - The trailing zero after the decimal point is significant.
7. A - $(0.2/86.4)\times 100\%=0.23\%$.
8. C - Radius percentage uncertainty is $(0.05/2.50)\times 100\%=2.0\%$; area depends on $r^2$, so it is $4.0\%$.
9. B - Timing many oscillations increases the measured interval, reducing the percentage effect of reaction-time uncertainty.
10. C - A systematic error produces a repeatable bias and is not removed by simple averaging.
11. C - The readings are close to one another but displaced from the accepted value.
12. B - The value should be quoted to the same decimal place as the uncertainty.
13. C - For subtraction, absolute uncertainties add: $\Delta L=0.1+0.1=0.2\mathrm{cm}$.
14. B - The component adjacent to $\theta$ is $F\cos \theta$; the opposite component is $F\sin \theta$.
15. C - Displacement requires magnitude and direction.
16. B - $R=\sqrt{6.0^2+8.0^2}=10.0\mathrm{m}$.
17. C - Sensible scale use improves graph readability and gradient accuracy.
18. B - Gradient unit is vertical-axis unit divided by horizontal-axis unit, $\mathrm{V}{\mathrm{A}}^{-1}$.
19. C - $8\mathrm{m}$ is nearer $10^1\mathrm{m}$ than $10^0\mathrm{m}$.
20. C - Homogeneity is necessary for a valid equation but does not prove correctness.

Review Figures

Figure: Use spread to judge precision and offset from the reference value to judge accuracy. Q11 tests the lower-left idea: readings can be close together but consistently displaced from the accepted value.

Figure: The uncertainty method depends on the mathematical structure of the calculated quantity. Q8 and Q13 use two different branches of this decision map: powers use percentage uncertainties, while subtraction uses absolute uncertainties.