Young's modulus relates stress and strain for the wire

Steps:

• Calculate area A = π (d/2)^2 = π (5 × 10^{-4})^2 ≈ 7.85 × 10^{-7} m².
• Calculate strain = ΔL / L = 2.7 × 10^{-3} / 5.2 ≈ 5.2 × 10^{-4}.
• Calculate stress = Y × strain = 360 × 10^9 × 5.2 × 10^{-4} ≈ 1.87 × 10^8 Pa.
• Calculate force F = stress × A ≈ 1.87 × 10^8 × 7.85 × 10^{-7} = 1.2 × 10^2 N.

Why B is correct:

• Hooke's law via Young's modulus Y = (F/A) / (ΔL/L) rearranges to F = Y A (ΔL/L), yielding 1.2 × 10^N N.

Why the others are wrong:

• A: Overestimates by roughly doubling the area (e.g., using d instead of d/2 without π adjustment).
• C: Results from omitting /4 in area formula, giving A ≈ π × 10^{-6} m² and F ≈ 5.0 × 10^N N.
• D: Arises from approximating L ≈ 5 m, increasing strain and F to ≈ 1.6 × 10^N N.

Final answer: B