Young's modulus relates stress and strain for the wire

Steps:

• Calculate stress σ = Y × Δε = (2.5 × 10^{11}) × (6.0 × 10^{-5}) = 1.5 × 10^7 Pa.
• Cross-sectional area A = F / σ = 34 / (1.5 × 10^7) = 2.3 × 10^{-6} m² (approx).
• For circular cross-section, A = π r^2, so r^2 = A / π ≈ 2.3 × 10^{-6} / 3.14 ≈ 7.3 × 10^{-7}.
• Thus r = √(7.3 × 10^{-7}) ≈ 8.5 × 10^{-6} m.

Why C is correct:

• It matches the radius from Y = (F / (π r^2)) / Δε, the definition of Young's modulus for uniaxial tension.

Why the others are wrong:

• A: From miscalculating A / π without square root.
• B: From taking r ≈ √(F / (Y Δε)) directly, ignoring π.
• D: From using diameter instead of radius in the area formula.

Final answer: C