A2 Daily A Level Physics question
In a tensile test to determine the Young modulus of a metal wire, a student later discovers two systematic issues: the micrometer used for the wire’s diameter overreads by 3%, and the scale used to read the extension under load underreads by 2%. All other measurements are accurate. When the student calculates the modulus from these data, what is the approximate percentage error and its direction?
Answer
The correct answer is C.
Correct: C — About -4% (underestimate). Diameter overreads by 3% so cross-sectional area (proportional to diameter squared) is about 6% too large, making the calculated modulus about 6% too small; the extension underreads by 2%, making the modulus about 2% too large; combined ≈ -6% + 2% = -4%. A Overlooks that area depends on diameter squared and that the two errors act in opposite directions; it incorrectly adds magnitudes to get a large positive error. B Ignores the squared effect of the diameter on area and/or the opposing sign from the extension underread. C Uses area ∝ d² and correctly combines -6% from area with +2% from extension to give -4% overall. D Assumes a 1:1 transfer from diameter to area or reverses one of the signs, giving the wrong direction and magnitude.