Question

A brass wire 1.8 m long at 27 °C is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of –39 °C, what is the tension developed in the wire, if its diameter is 2.0 mm? Co-efficient of linear expansion of brass = 2.0 × 10^–5 K^–1; Young’s modulus of brass = 0.91 × 10¹¹ Pa.

Solution

Given,
Initial temperature, T₁ = 27°C
Length of the brass wire at T₁, l = 1.8 m
Final temperature, T₂ = –39°C
Diameter of the wire, d = 2.0 mm = 2 × 10^–3 m
Tension developed in the wire = F

Coefficient of linear expansion of brass, α = 2.0 × 10^–5 K^–1
Young’s modulus of brass, Y = 0.91 × 10¹¹ Pa

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