Extension using Young's modulus Steps:

• Compute cross-sectional area: A = π (d/2)^2 = π (1.2 × 10^{-3}/2)^2 = π (6 × 10^{-4})^2 ≈ 1.13 × 10^{-6} m².
• Compute stress: σ = F/A = 37 / (1.13 × 10^{-6}) ≈ 3.27 × 10^7 Pa.
• Compute strain: ε = σ / Y = 3.27 × 10^7 / (1.1 × 10^{11}) ≈ 2.97 × 10^{-4}.
• Compute extension: ΔL = ε × L = 2.97 × 10^{-4} × 3.6 ≈ 0.00107 m = 0.97 mm (rounded).

Why C is correct:

• Young's modulus Y = (F/A) / (ΔL/L) rearranges to ΔL = (F L) / (A Y), yielding 0.97 mm for the given values.

Why the others are wrong:

• A: Assumes radius equals diameter, quadrupling A and reducing ΔL by factor of 4.
• B: Likely from underestimating stress by using incorrect area (e.g., d instead of d/2).
• D: Ignores area in denominator, vastly overestimating extension.

Final answer: C