A wire of length L, area of cross-section A is hanging from a field support. The length of the wire changes to L₁ when mass M is suspended from its free end. The expression for Young's modulus is:
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A wire of length L, area of cross-section A is hanging from a field support. The length of the wire changes to L₁ when mass M is suspended from its free end. The expression for Young's modulus is:

G1 Physics · Accepted Answer

Step 1: The extension produced by the hanging mass is ΔL = L₁ − L. Step 2: The force in the wire is F = Mg, and longitudinal stress is σ = Mg/A. Step 3: Longitudinal strain is ε = ΔL/L = (L₁ − L)/L. Step 4: Young's modulus is Y = σ/ε. Step 5: Y = (Mg/A) ÷ [(L₁ − L)/L] = MgL/[A(L₁ − L)]. Final answer: (C) MgL/[A(L₁ − L)].