Strain from Young's modulus formula

Steps:

• Radius r = diameter/2 = 1.6 × 10^{-3} m / 2 = 8 × 10^{-4} m
• Area A = π r^2 ≈ 3.14 × (8 × 10^{-4})^2 = 3.14 × 6.4 × 10^{-7} = 2.0 × 10^{-6} m²
• Stress σ = force / A = 430 / 2.0 × 10^{-6} = 2.15 × 10^8 Pa
• Strain ε = σ / Y = 2.15 × 10^8 / (130 × 10^9) = 1.65 × 10^{-3}

Why D is correct:

• Strain equals stress divided by Young's modulus within the proportionality limit, yielding ≈ 2 × 10^{-3} with standard approximations.

Why the others are wrong:

• A. From error using A = π d² (ignores /4 factor, overestimates area).
• B. From error using A = d² (ignores π and /4, overestimates area).
• C. From error using A = (d/2)² (ignores π, underestimates area).

Final answer: D