The maximum elongation of a steel wire of length l if the elastic limit of steel and its Young's modulus, respectively, are 8 × 10⁸ N m⁻² and 2 × 10¹¹ N m⁻², is:
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The maximum elongation of a steel wire of length l if the elastic limit of steel and its Young's modulus, respectively, are 8 × 10⁸ N m⁻² and 2 × 10¹¹ N m⁻², is:

G1 Physics · Accepted Answer

Step 1: At the elastic limit, the maximum tensile stress is σₘₐₓ = 8 × 10⁸ N m⁻². Step 2: Young's modulus is Y = σ/ε, so maximum strain εₘₐₓ = σₘₐₓ/Y. Step 3: εₘₐₓ = (8 × 10⁸)/(2 × 10¹¹) = 4 × 10⁻³. Step 4: Maximum extension is Δlₘₐₓ = εₘₐₓ l = (4 × 10⁻³)l. Step 5: For l = 1 m, Δlₘₐₓ = 4 × 10⁻³ m = 4 mm. Printed key: (D) 4 mm. Caution: the scanned question denotes the length by l but does not explicitly give l = 1 m; the numerical answer needs that assumption.