A2 Daily A Level Physics question
In a required-practical to determine the Young modulus of a metal wire, a student plots force F against extension x and uses the gradient of the straight line as a measure of the wire’s stiffness. The wire is then replaced by one of the same material but with half the diameter and three times the original length. All other parts of the setup and the plotting method are unchanged. Which statement about the new F–x gradient is correct? Explain your choice by considering how wire dimensions affect the F–x gradient.
Answer
The correct answer is B.
Correct: B — It decreases to one-twelfth of its original value. For a given material, the F–x gradient is proportional to cross-sectional area and inversely proportional to length, so halving diameter reduces area by a factor of 4 while tripling length adds a factor of 1/3, giving an overall factor of (1/4)×(1/3) = 1/12. A says it increases, which reverses the combined effects of smaller area and longer length. B is the correct combined scaling, as shown. C accounts only for the reduced area (1/4) and ignores the extra factor of 1/3 from the increased length. D accounts only for the increased length (1/3) and ignores the additional 1/4 from the reduced area.