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AS Daily A Level Physics question

2026-04-26 OCR A Materials (M3) Module 3.4 Materials: Young modulus; stress–strain; practical determination Module 1.2.1 Practical skills: data analysis; systematic errors; gradients and proportional reasoning

In a lab to determine the Young modulus of a metal wire, a student measures the wire’s diameter with a micrometer, its original length L, then hangs a range of loads and plots extension against load; they use the straight-line gradient and their measured L and cross-sectional area to calculate the modulus. Unknown to them, the micrometer reads the diameter 5% too small, and the extension scale has a constant +0.20 mm zero offset that is not corrected. Which statement must be true about the calculated modulus compared with the true value, and why?

  1. A Overestimated by about 11%, because using a diameter 5% too small makes the area about 10% too small; a constant zero offset in extension does not change the slope of extension versus load. (correct)
  2. B Underestimated by about 11%, because a smaller measured diameter makes the wire seem more stretchy and the zero offset increases measured extensions.
  3. C Overestimated by about 5%, because the diameter error scales directly and the zero offset partially cancels it when taking the slope.
  4. D Essentially unchanged, because both the diameter and extension errors shift the graph without altering the calculation.

Answer

The correct answer is A.

Correct: A — Overestimated by about 11%, because using a diameter 5% too small makes the area about 10% too small; a constant zero offset in extension does not change the slope of extension versus load. A The area scales with the square of diameter, so 0.95^2 = 0.9025 makes the area 9.75% too small; since E ∝ 1/A, the calculated modulus is about 1/0.9025 ≈ 1.11 times the true value, and a constant offset only shifts the intercept. B This reverses the sign: a smaller measured area increases, not decreases, the calculated modulus, and a constant offset does not increase the gradient. C This treats area as proportional to diameter (5%) and assumes cancellation by the offset; in fact area depends on diameter squared and the offset does not affect the slope. D A 5% diameter error yields about an 11% effect through area, so the result is not essentially unchanged; only the zero offset alone would leave the gradient (and thus the modulus) unaffected.

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