AS Daily A Level Physics question
In a lab to determine a wire’s stiffness, a student measures the extension directly with a dial gauge (±0.01 mm). With a 10 N load on a 1.0 m wire of diameter 0.50 mm, the extension is 0.20 mm. They can instead use a 2.0 m wire of the same material and diameter, keeping the same load range and the same gauge. Assuming the wire stays in its linear elastic region, which statement must be true if they swap to the 2.0 m wire?
Answer
The correct answer is B.
Correct: B — The extension for 10 N becomes 0.40 mm, so the percentage uncertainty in extension for that load is about 2.5%, half of before. Doubling the length doubles the extension for the same load (0.20 mm → 0.40 mm), so with ±0.01 mm the relative uncertainty falls from 0.01/0.20 ≈ 5% to 0.01/0.40 ≈ 2.5%. A The extension does not stay at 0.20 mm; for the same force and diameter, extension scales with length, so it doubles, not stays the same. B This matches the proportional increase in extension with length and the consequent halving of percentage uncertainty with the same absolute reading uncertainty. C The extension does not decrease to 0.10 mm; making the wire longer increases, not decreases, the extension under a given load. D Although the absolute resolution is unchanged, the reading is larger (0.40 mm), so the percentage uncertainty decreases rather than staying the same.