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AS Daily A Level Physics question

2026-07-03 OCR A Foundations of Physics (M2) Module 2.1 Physical quantities and units (derived quantities, proportional reasoning) Module 2.2 Making measurements and analysing data (uncertainties, percentage errors)

In a lab, a student estimates the density of a flat metal coin by measuring its mass and its diameter and thickness. The balance and thickness gauge are well calibrated, but the calipers used for the diameter have a +1.0% zero error, making all diameter readings 1.0% too high. Which statement must be true about the percentage error in the calculated density?

  1. A The calculated density is about 1.0% lower, because volume changes in direct proportion to the diameter.
  2. B The calculated density is about 2.0% lower, because volume depends on the square of the diameter. (correct)
  3. C The calculated density is about 1.0% higher, because the measured area is underestimated.
  4. D The calculated density is about 2.0% higher, because both area and thickness are overestimated.

Answer

The correct answer is B.

Correct: B — The calculated density is about 2.0% lower, because volume depends on the square of the diameter. A assumes volume changes linearly with diameter; since area ∝ d^2, a +1.0% diameter error gives about +2.0% volume error, not 1.0%. B is correct because a +1.0% error in d leads to ≈+2.0% in volume (d^2), so density m/volume is ≈2.0% lower. C is wrong because an overestimated diameter makes the area overestimated, not underestimated, so density cannot be higher. D is wrong because thickness is measured accurately; only diameter is biased, so the sign is wrong and the effect should be a decrease, not an increase.

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