Answer: Four times more likely to cross its elastic limit due to higher stress.
- A Equally safe, since the cross-sectional area change has no effect on stress
- B Four times more likely to cross its elastic limit due to higher stress
- C Safer because the thinner wire stretches less under the same load
- D Unaffected since strain depends only on the material, not the geometry
Correct answer: B. Four times more likely to cross its elastic limit due to higher stress
Explanation: Halving diameter quarters the cross-sectional area (A ∝ d²), so for the same load, stress (F/A) becomes four times larger, making it much more likely to exceed the elastic limit.
A typical stress-strain curve: the initial straight line (Hooke's Law region, slope = Young's modulus) ends at the elastic limit; beyond the yield point, deformation becomes permanent, peaking at the ultimate tensile strength before the wire finally fractures.
Concept context
Stress, strain, Hookes law, and the elastic moduli that describe how solids deform and recover under load.