Q.

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

Y A α ΔT

b

Yα ΔT/A

c

A α ΔT/Y

d

YA/α ΔT

answer is A.

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Detailed Solution

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 Δl=αlΔTStrain in wire =(Δl/l)=αΔTNow Y= stress  strain =(F/A)Δl/l=FlAΔlSo, tension in the wire is given by F=Y A Δll=Y A α ΔT
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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