Question

A steel wire of length L at 40^∘C is suspended from the ceiling and a mass m is hung from its free end. The wire is cooled from 40^∘C to 30^∘C to regain its original length L. The coefficient of linear expansion of steel is 10⁻5/^∘C. Young’s modulus of steel is 10¹1N/m² and radius of the wire is 1mm. Assume diameter of the wire. Then the value of m in kg is nearly

• A. 1
• B. 2
• C. 3
• D. 5

Hint:

If a wire is prevented from changing length during temperature change: stress = Y α Δ T

Answer 1

The Correct Option is C

Step 1: Thermal strain due to cooling: strain = α Δ T = 10⁻5 × 10 = 10⁻4 Step 2: Stress developed to keep length unchanged: stress = Y α Δ T = 10¹1 × 10⁻4 = 10⁷N/m² Step 3: Cross-sectional area of wire: A = π r² = π (10⁻3)² ≈ 3.14 × 10⁻6m² Step 4: Tension in the wire: T = stress × A ≈ 10⁷ × 3.14 × 10⁻6 ≈ 31.4N Step 5: Since T = mg: m = (31.4)/(9.8) ≈ 3.2 kg boxedm ≈ 3kg