AQA A Level Physics: Measurements and Their Errors — Practice Questions

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — examination boards hold copyright in their own papers. Use these alongside the official past papers available free from your board.

Related: Measurements and Their Errors revision notes

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Questions

1. Distinguish between accuracy and precision, and give an example of data that is precise but not accurate. [3]

2. Distinguish between random and systematic error, and state how each can be reduced. [4]

3. A student times 20 oscillations of a pendulum three times: 31.2 s, 31.5 s, 31.1 s.

(a) Calculate the mean period of one oscillation. [3] (b) Explain why 20 oscillations are timed rather than one. [2] (c) The stopwatch reads to 0.01 s but the student’s reaction time is about 0.2 s. State which limits the measurement and what kind of error this is. [2]

4. A resistance is calculated from V = 4.85 ± 0.05 V and I = 0.42 ± 0.01 A.

(a) Calculate the resistance. [1] (b) Calculate the percentage uncertainty in V and in I. [2] (c) Calculate the percentage and absolute uncertainty in R. [3] (d) State the result to an appropriate number of significant figures. [1]

5. A graph of y against x should pass through the origin but has a positive intercept, with the expected gradient.

(a) State the type of error indicated. [1] (b) Suggest one possible experimental cause. [1] (c) Explain why repeating the readings would not remove it. [2]

6. Describe how to find the uncertainty in the gradient and in the intercept of a straight-line graph using error bars. [4]

7. Distinguish between repeatable and reproducible results. [2]

8. A sphere’s radius is measured with a percentage uncertainty of 2%. Since volume is proportional to r³, find the percentage uncertainty in the calculated volume. [2]

9. Two data points have overlapping error bars. What can be concluded about the difference between them? [1]

10. A student measures the diameter of a wire five times with a micrometer: 0.82, 0.84, 0.81, 0.83, 0.82 mm.

(a) Calculate the mean diameter and the uncertainty using the range method. [2] (b) The wire’s length is 1.500 m ± 0.002 m. The resistivity is calculated from ρ = RA/L, where A is the cross-sectional area. State which of the two measurements (diameter or length) contributes the larger percentage uncertainty to ρ, and explain why. [3]

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Answers

1. Accuracy is closeness to the true value; precision is how closely repeated readings agree with each other [1] [1]. A balance with a zero error gives tightly grouped readings that are all wrong by the same amount [1]. Repeatability and reproducibility are related but distinct ideas: repeatable means the same result on repeating with the same method and equipment, while reproducible means the same result with a different method or person.

2. Random error causes scatter about the true value [1]; reduced by repeating and averaging [1]. Systematic error shifts all readings in the same direction [1]; reduced only by recalibrating or zeroing the instrument, or changing technique [1].

3. (a) Mean of 20 oscillations = (31.2 + 31.5 + 31.1) ÷ 3 = 31.27 s [1] [1] T = 31.27 ÷ 20 = 1.56 s [1]. (b) The absolute uncertainty from reaction time is fixed [1], so timing a longer interval makes it a much smaller percentage of the reading [1]. (c) The reaction time limits it [1]; this is primarily a random error, since it varies from timing to timing, though it becomes systematic if the student consistently starts or stops early or late [1].

4. (a) R = 4.85 ÷ 0.42 = 11.55 Ω [1]. (b) V: (0.05 ÷ 4.85) × 100 = 1.03% [1]. I: (0.01 ÷ 0.42) × 100 = 2.38% [1]. (c) For division, percentage uncertainties add: 1.03 + 2.38 = 3.41% [1] [1] Absolute = 0.0341 × 11.55 = ±0.39 Ω [1]. (d) R = 11.6 ± 0.4 Ω [1].

5. (a) Systematic error [1]. (b) A zero error on the instrument, or a consistent offset such as failing to account for the mass of a container [1]. (c) Repeating reduces random scatter about the line [1], but every reading is shifted by the same amount, so the intercept remains [1].

6. Draw the steepest and shallowest lines that still pass through all the error bars [1] [1]. The uncertainty in the gradient is half the difference between these two gradients [1]. The uncertainty in the intercept is found the same way: half the difference between the two lines’ intercepts [1].

7. Repeatable — the same result is obtained on repeating with the same method and equipment [1]. Reproducible — the same result is obtained with a different method or by a different person [1].

8. Raising to a power multiplies the percentage uncertainty by that power [1]: % uncertainty in V = 3 × 2% = 6% [1].

9. The difference between them may not be significant [1] — overlapping error bars mean the true values could plausibly be equal.

10. (a) Mean = (0.82 + 0.84 + 0.81 + 0.83 + 0.82) ÷ 5 = 0.824 mm [1]. Range = 0.84 − 0.81 = 0.03 mm; uncertainty = 0.03 ÷ 2 = ±0.015 mm [1]. (b) Percentage uncertainty in diameter = (0.015 ÷ 0.824) × 100 = 1.8% [1]; percentage uncertainty in length = (0.002 ÷ 1.500) × 100 = 0.13% [1]. The diameter contributes the larger percentage uncertainty [1] — and because A depends on the diameter squared, the diameter’s contribution to the uncertainty in ρ is doubled again (to roughly 3.6%), making it by far the dominant source of uncertainty in the final result.

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Where marks are usually lost

• Swapping accuracy and precision.
• Saying repeats reduce systematic error.
• Adding absolute uncertainties when dividing.
• Quoting a result to more significant figures than the uncertainty justifies.
• Confusing repeatable (same method, same person) with reproducible (different method or person).
• Forgetting to multiply, not add, the percentage uncertainty when a quantity is raised to a power.
• Declaring a definite difference between two data points whose error bars overlap.
• Forgetting that a squared quantity in a formula doubles its percentage-uncertainty contribution relative to a linear one.