AS Daily A Level Physics question

2026-01-28 OCR A Materials: mechanical properties and practical measurement (Module 3) OCR-A Module 3 (Mechanics and Materials): 3.4 Materials — tensile properties (stress, strain) and practical determination of stiffness/Young modulus using wire extension OCR-A Module 1: Practical skills — planning and evaluating measurements (wire extension method)

In a lab test of elastic extension, a student hangs a 10 N load from a steel wire and measures its extension with a pointer and ruler. With a 2.0 m wire of diameter 0.50 mm, the extension is 0.40 mm and the wire remains elastic. They repeat with the same load using a 1.0 m wire of the same material but 1.0 mm diameter. Assuming elastic behaviour and negligible heating, what extension should they expect?

A 0.20 mm
B 0.10 mm
C 0.050 mm (correct)
D 0.80 mm

Answer

The correct answer is C.

Correct: C — 0.050 mm. A 0.20 mm — this considers only halving the length, ignoring that doubling diameter increases area by four, further reducing the extension. B 0.10 mm — this treats area as doubling with diameter instead of quadrupling, so it underestimates how much the thicker wire reduces extension. C 0.050 mm — for the same load in the elastic range, extension scales with length and inversely with cross-sectional area, so halving length (×1/2) and doubling diameter (area ×4) gives an overall factor of 1/8: 0.40 mm ÷ 8 = 0.050 mm. D 0.80 mm — this reverses the dependence, as a larger diameter (greater area) decreases, not increases, the extension under the same load.

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