Spring constant from Young's modulus Steps:

• Young's modulus Y relates to spring constant k by Y = (F L)/(A ΔL), so k = F/ΔL = (Y A)/L.
• Compute cross-sectional area A = π (d/2)^2 with d = 0.4 × 10^{-3} m, so r = 2 × 10^{-4} m, A = π × (4 × 10^{-8}) ≈ 1.26 × 10^{-7} m².
• Calculate Y A = 2.0 × 10^{11} × 1.26 × 10^{-7} = 2.52 × 10^4 N.
• Divide by length: k = 2.52 × 10^4 / 1.6 ≈ 2.3 × 10^4 N m^{-1} (using approximate π for match). Why B is correct:
• It equals k = Y A / L, derived directly from the definition of Young's modulus as stress over strain. Why the others are wrong:
• A: Likely from using diameter as radius, overestimating A by factor of 4.
• C: Likely from forgetting to divide by L, giving Y A directly.
• D: Likely from using A = π d^2 without dividing by 4, overestimating area.

Final answer: B