Elastic strain from Hooke's law

Steps:

• Calculate cross-sectional area: A = π (d/2)^2 = π (0.25 × 10^{-3})^2 ≈ 1.96 × 10^{-7} m².
• Compute stress: σ = tension / A = 20 / 1.96 × 10^{-7} ≈ 1.02 × 10^8 Pa.
• Find strain: ε = σ / Young's modulus = 1.02 × 10^8 / 2.0 × 10^{11} = 5.1 × 10^{-4}.
• Percentage contraction: ε × 100% = 5.1 × 10^{-2}%.

Why D is correct:

• Hooke's law defines strain as ΔL/L, so percentage change is strain × 100%, yielding 5.1 × 10^{-2}%.

Why the others are wrong:

• A: Underestimates by factor of ~400, likely from area error and omitting ×100%.
• B: Gives raw strain without converting to percentage.
• C: Overestimates strain by factor of ~100, possibly from incorrect area (e.g., using diameter instead of radius).

Final answer: D