Question

A steel wire of uniform cross-section of 1 m² is heated to 70°C and stretched by tying its two ends rigidly. What is the change in the tension of the wire when the temperature falls from 70°C to 35°C? Coefficient of linear expansion of steel is 1.1 10^-5 /°C and Young’s modulus is 2.010¹¹N/m².

• A. 250N
• B. 116N
• C. 77N
• D. 28N

Answer 1

Answer: (C)

77N

Answer 2

The tension produced in a stretched wire due to fall in temperature by ∆t is.

F = YA α∆t

Where Y and α are the Young’s modulus and coefficient of linear expansion of the material of the wire and A is the cross-sectional area.

Here Y = 2.010¹¹N/m²

A = 1.0 mm² = 1.010^-6m²

α = 1.110^-5/⁰C

∆t = (70 – 35) = 35⁰C

∴ F = 2.010¹¹ (1.0 10^-6) (1.110^-6) 35 = 77N