A2 Daily A Level Physics question
In a Young modulus practical, a student measures the gradient of a load–extension graph for a metal wire of length L and diameter d (small elastic extensions). They then replace it with a wire of the same material but length 2L and diameter 0.5d, using the same load range. Which statement about the new graph's gradient is correct, and why?
Answer
The correct answer is A.
Correct: A — It decreases by a factor of 8, because extension for a given load scales with length and inversely with cross-sectional area (area ∝ d^2). A is consistent with extension per unit force increasing eightfold (2 from length and 4 from area), so the gradient (force per extension) must reduce by 8. B reverses the inference: reducing area and increasing length both reduce stiffness, so the gradient cannot increase. C underestimates the effect by treating area as proportional to diameter (not diameter squared) and also ignores the doubling of length. D confuses series/parallel reasoning: making a wire longer is like adding springs in series (less stiff), and halving the diameter further reduces stiffness, so the gradient would not be steeper.