A2 Daily A Level Physics question
In a Young modulus experiment with a thin metal wire, the cross-sectional area is obtained from micrometer diameter readings. The mean diameter is 0.50 mm with a percentage uncertainty of 2.0%. Assuming this dominates, what is the percentage uncertainty in the calculated cross-sectional area?
Answer
The correct answer is B.
Correct: B — 4.0%. Area depends on the square of diameter, so the percentage uncertainty doubles: 2.0% × 2 = 4.0%. A 2.0% — assumes the area’s uncertainty is the same as the diameter’s, ignoring the square dependence. B 4.0% — correctly applies the rule that percentage uncertainty in a squared quantity is doubled. C 1.0% — wrongly halves the uncertainty because diameter is divided by 2 to get radius; constant factors do not change percentage uncertainty. D 8.0% — overestimates as if area depended on the fourth power of diameter or by compounding the uncertainty twice.