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Question

# A brass wire 1.8 m long at 27 is held taut with negligible tension between two rigid supports. Diameter of the wire is 2 mm, its coefficient of linear expansion, αBrass=2×10−5−1 and its young's modulus, YBrass=9×1010Nm−2 , If the wire is cooled to a temperature −39, 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/AΔL/L As ΔL=LαΔT∴Y=FAαΔTorF=YAαΔTHere, α=2.0×10−5−1,Y=9×1010Nm2 A=π(1×10−3)2m2,ΔT=66∴F=9×1010×π(1×10−3)2×2.0×10−5×66=3.7×102N

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