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A wire of length L₁, area of cross section A is hanging from a fixed 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:

1. Mg(L₁ − L) / AL
2. MgL / AL₁
3. MgL / A(L₁ − L)
4. MgL₁ / AL

Correct answer: MgL / A(L₁ − L)

Solution

Young's modulus (Y) is defined as stress divided by strain. Stress is the force per unit area (Mg/A), and strain is the relative change in length ((L₁ − L)/L). Substituting these into the formula Y = (stress)/(strain), we get Y = (Mg/A) / ((L₁ − L)/L), which simplifies to Y = MgL / A(L₁ − L).

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