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

Question

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

Infinity Learn · Accepted Answer

Let I be the length of the wire at temperature T. If ∆l be the contraction in length when the temperature falls by ∆T, then Δ$$l=$$αlΔTStrain in wire $$=($$Δ$$l/l)=$$αΔTNow $$Y=$$ stress  strain $$=(F/A)$$Δ$$l/l=FlA$$ΔlSo, tension in the wire is given by $$F=Y$$ A Δ$$ll=Y$$ A α ΔT

A wire of cross-sectional area A at temperature T is held taut with 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

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A wire of cross-sectional area A at temperature T is held taut with 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

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Ready to Test Your Skills?

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A wire of cross-sectional area A at temperature T is held taut with 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