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Question

# A brass wire 1.8 m long at 27oC is held taut with negligible tension between two rigid supports Diameter of the wire is 2mm, its coefficient of linear expansion,αBrass=2×10−5oC−1 and its Young's modulus, YBrass=9×1010Nm−2,If the wire is cooled to temperature −39oC, tension developed in the wire is :

A
2.7×102N
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B
3.7×102N
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C
4.7×102N
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D
5.7×102N
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Solution

## The correct option is B 3.7×102NLet F be tension developed in the wire.∴Y=F/A△L/LAs △L=Lα△T∴Y=FAα△T or F=YAα△THere , α=2.0×10−5oC−1,Y=9×1010Nm−2A=π(1×10−3)2M2 △T=66oC∴F=9×1010×π(1×10−3)2×2.0×10−5×66⇒3.7×102N

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