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AS Daily A Level Physics question

2026-05-13 OCR A Uncertainties & percentage errors (AS Practical Skills) Module 1: Development of practical skills — 1.2.3 Analysis of data (uncertainties and percentage errors) Module 2: Foundations of physics — 2.1.2 Physical quantities and units (estimating and combining uncertainties) Mathematical skills: percentage/ratio reasoning in uncertainty propagation (AS)

In a lab test of a small winch, a student estimates its power using P = m g h / t. They use m = 0.200 kg measured with a balance of ±0.001 kg, h = 0.600 m found as the difference between two metre-rule readings each with ±0.001 m, and t = 3.0 s with a timing uncertainty of ±0.10 s (reaction-time limited). The student can change only one aspect for a second trial. Which option gives the greatest reduction in the percentage uncertainty in P?

  1. A Time five identical lifts back-to-back so the total t ≈ 15 s; with ±0.10 s, the percentage uncertainty in t falls by a factor of 5 (from about 3.3% to about 0.7%), giving the largest reduction overall. (correct)
  2. B Double the mass to 0.400 kg; with ±0.001 kg, the percentage uncertainty in m halves (to about 0.25%), so this gives the biggest improvement.
  3. C Replace the metre rule with a 0.5 mm resolution rule for each height reading; the uncertainty on h (difference of two readings) drops from ±0.002 m to ±0.001 m (about 0.33% to about 0.17%), giving the largest improvement.
  4. D Repeat the lift three times and average; this reduces uncertainties uniformly, so it will have the greatest effect.

Answer

The correct answer is A.

Correct: A — Time five identical lifts back-to-back so the total t ≈ 15 s; with ±0.10 s, the percentage uncertainty in t falls by a factor of 5 (from about 3.3% to about 0.7%), giving the largest reduction overall. A The timing contributes about 0.10/3.0 ≈ 3.3%, far larger than mass (≈0.5%) and height (≈0.002/0.600 ≈ 0.33% since h is a difference of two readings), so increasing t by 5 cuts the dominant term to ≈0.7%, reducing the overall percentage uncertainty by roughly 2.6%. B Although doubling m halves its percentage uncertainty to ≈0.25%, mass was not dominant, so the overall reduction is only about 0.25%, much smaller than A. C Improving the ruler halves the height term from ≈0.33% to ≈0.17%, but this change is still much smaller than cutting the dominant timing term from ≈3.3% to ≈0.7%. D Averaging three trials reduces random timing uncertainty by about √3, giving ≈0.10/√3 ≈ 0.058 s (≈1.9%), which is a smaller improvement than timing five lifts; it also does not reduce systematic or resolution-limited effects equally.

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