A2 Daily A Level Physics question
In a lab to determine the stiffness of a steel wire, a student measures the wire’s diameter with a micrometer that reads 0.02 mm too high (positive zero error). The true diameter is 0.50 mm, but the student does not correct the error. All other measurements (length, load, extension) are accurate. Estimate the percentage error in the calculated Young modulus due to this uncorrected zero error, and state whether the modulus is over- or under-estimated.
Answer
The correct answer is A.
Correct: A — The calculated Young modulus is about 8% too low. A is correct because the diameter is over-read by 0.02/0.50 = 4%, so the area (∝ diameter²) is overestimated by about 8%, placing a larger value in the denominator and making the modulus ≈8% smaller. B is wrong because it treats the error as linear in diameter rather than squared area. C is wrong because it both assumes a linear effect and gets the sign wrong (a larger area makes the modulus smaller, not larger). D is wrong because it applies the squared effect but gets the sign wrong—the modulus would be underestimated, not overestimated.