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A steel wire of length L at 40°C hangs from a ceiling, and a mass m is attached to its lower end. The wire is then cooled from 40°C to 30°C, after which it returns exactly to its original length L. Given the linear thermal expansion coefficient of steel = 10⁻⁵ /°C, Young's modulus = 10¹¹ N/m², wire radius = 1 mm, and L much greater than the diameter, the value of m (in kg) is nearest to:

1. 1
2. 10
3. 100
4. 1000

Correct answer: 1

Solution

Equating elastic stretch and thermal contraction gives m = α*ΔT*A*Y/g = pi ≈ 3.14 kg; among the order-of-magnitude options the nearest value is 1.

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