AS Daily A Level Physics question
In a lab determination of Young modulus using a metal wire, a student wants to increase the measured extension to reduce percentage uncertainty. They switch to a wire of the same material that is twice the original length and has half the original diameter. For the same applied force, what happens to the extension?
Answer
The correct answer is B.
Correct: B — Increase by a factor of 8. For the same material and force, extension is proportional to length divided by cross-sectional area; doubling the length gives ×2 and halving the diameter quarters the area (×4), so overall ×8. A ignores the area change and considers only the doubled length. B is the only option that accounts for both the doubled length and the quartered area. C treats area as proportional to diameter (factor 2) rather than diameter squared. D reverses the proportionality, implying a decrease despite longer length and smaller area both increasing extension.