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Question

# A wire of cross-sectional area A at temperature t is held taut with a negligible tension between two rigid supports. If the wire is cooled to a temperature (t−Δt), what tension is developed in the wire? The coefficient of linear expansion is α and Young's modulus of the wire is Y.

A

YAαΔt

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B

YαΔtA

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C

AαΔtY

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D

YAαΔT

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Solution

## The correct option is A YAαΔt Let l be the length of the wire at temperature t and Δl be the contraction in the length as the temperature falls by Δt. Then, Δl=αlΔt ∴ Strain in the wire (Δll)=αΔt Now, young's modulus, Y=StressStrain=FAΔll ∴ Tension in the wire is F=YAΔll=YAαΔt and the correct choice is (a).

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