AS Daily A Level Physics question
In a lab tensile test, two uniform circular wires are hung vertically and loaded in their elastic regions until each extends by exactly 1.0 mm. Wire S (steel) is 1.0 m long with diameter 0.50 mm and requires a 20 N load. Wire P (polymer) is 0.50 m long with diameter 1.0 mm and requires a 5.0 N load. Assuming uniform cross-sections, which statement about the ratio of their Young moduli Y_S / Y_P must be true?
Answer
The correct answer is D.
Correct: D — Y_S / Y_P = 32. With the same extension, the modulus scales as (force × original length) divided by cross-sectional area. Using ratios: (20/5) × (1.0/0.50) × (A_P/A_S) with A_P/A_S = (1.0/0.50)^2 = 4 gives 4 × 2 × 4 = 32. A uses only the force ratio and ignores both length and area effects. B includes the area effect but ignores the length difference, giving 4 × 4 = 16. C includes the length effect but ignores the area difference, giving 4 × 2 = 8. D accounts for both the length and the area (via diameter squared), yielding the correct factor 32.