Question

A steel wire of length L at 40°C is suspended from the ceiling and carries a mass m 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 is 10⁻⁵/°C, Young’s modulus of steel is 10¹¹ N m⁻², and the radius of the wire is 1 mm. The value of m in kg is nearly

• A. 1
• B. 2
• C. 3
• D. 5

Hint:

Prevented thermal expansion produces stress: σ = YαΔ T.

Answer 1

The Correct Option is C

Step 1: Thermal strain ε = α Δ T = 10⁻5× 10
Step 2: Stress σ = Yε = 10¹1× 10⁻4 = 10⁷ N m⁻2
Step 3: Force F = σ A = 10⁷ × π(10⁻3)² ≈ 31 N
Step 4: m = F/g ≈ 3kg