AS Daily A Level Physics question
In a lab to estimate the stiffness of a metal using a wire, a student measures the small extension under a fixed 100 N load with a ruler (±0.5 mm reading uncertainty). They replace the wire with another of the same material and original length but twice the diameter, keeping the load the same. Which statement must be true?
Answer
The correct answer is A.
Correct: A — The extension becomes one-quarter, so the percentage uncertainty from the ±0.5 mm reading roughly quadruples. A is correct because extension is inversely proportional to cross-sectional area and area ∝ diameter², so doubling diameter makes area 4× larger and extension 4× smaller; with the same absolute reading uncertainty, the percentage uncertainty is 4× larger. B is wrong because it assumes extension ∝ 1/diameter (not 1/diameter²) and also claims the percentage uncertainty would get smaller rather than larger. C is wrong because a thicker wire does not extend more under the same load; the direction is reversed. D is wrong because extension depends on geometry (area), not just load and material, so it cannot be unchanged.