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A tungsten wire of diameter 0.5 mm is stretched taut (with negligible initial tension) between two rigid supports at 40 deg C. Find the tension developed in the wire when its temperature drops to 20 deg C. Take the coefficient of linear expansion of tungsten as 4.5 * 10⁻⁶ per deg C and Young's modulus as 3.45 * 10¹¹ N/m².

1. 0.6097 N
2. 3.097 N
3. 5.097 N
4. 7.097 N

Correct answer: 0.6097 N

Solution

A clamped wire that is cooled develops tension because the thermal strain alpha*(delta T) is converted into elastic strain. The restoring force equals the cross-sectional area times Young's modulus times that strain.

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