AS Daily A Level Physics question
In a required practical to determine the Young modulus of a metal wire that obeys Hooke’s law for the loads used, a student first marks two points 1.00 m apart on the wire and measures the extension between the marks under a constant load using a scale with 0.10 mm resolution. They then repeat the measurement with the marks 2.00 m apart, keeping the same wire, diameter and load. Which statement must be true for the second run?
Answer
The correct answer is B.
Correct: B — The extension doubles and the percentage uncertainty in that extension halves, with the stress unchanged. A fixed load and cross-sectional area mean stress is unchanged, while doubling gauge length doubles extension (so with the same 0.10 mm resolution, the percentage uncertainty is halved). A Stress depends on force and cross-sectional area, not on length, so it does not double; the extension does double but the stress part is wrong. B This is correct because ΔL is proportional to original length for the same load and area, and a larger ΔL reduces percentage uncertainty by a factor of two with the same resolution. C For the same stress, strain stays the same (ΔL doubles but so does L), so neither strain nor Young modulus doubles. D Extension does not stay the same; it increases in proportion to gauge length, so the premise is false.