A wire of original length 2.0 m and cross-sectional area 1.0 × 10⁻⁶ m² stretches by 1.0 mm under a tension of 100 N. Calculate Young's modulus of elasticity for the wire material.

Answer and explanation

Correct answer: C. 2.0 × 10¹¹ N/m²

  1. Step 1: Tensile stress: σ = F / A = 100 / (1.0 × 10⁻⁶) = 1.0 × 10⁸ N/m². Step 2. Tensile strain: ε = ΔL / L = (1.0 × 10⁻³) / 2.0 = 5.0 × 10⁻⁴. Step 3. Young's modulus: E = σ / ε = (1.0 × 10⁸) / (5.0 × 10⁻⁴) = 2.0 × 10¹¹ N/m². Answer: 2.0 × 10¹¹ N/m². Why not the others: 1.0 × 10¹¹ N/m² uses L = 1.0 m; 5.0 × 10¹⁰ N/m² inverts strain; 4.0 × 10¹¹ N/m² doubles length.

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