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A steel wire of cross-sectional area 0.5...

A steel wire of cross-sectional area `0.5mm^2` is held between two fixed supports. If the wire is just taut at `20^@C`, determine the tension when the temperature falls to `0^@C`. Coefficient of linear expansion of steel is `1.2 xx 10^(-5 @)C(-1)` and its Young's modulus is `2.0 xx 10^11 N m^(-2)`.

Text Solution

Verified by Experts

If `L` be the original length, change in length `/_\l` is given by
`/_\l=Lalphat`
Therefore, longitudinal strain `(/_\l)/L=alphat`
`12xx10^(-6)xx20=24xx10^(-5)`
Tensile stress in the wire `=Yxx"Strain"`
`=21xx10^(11)xx24xx10^(-5)`
`=5.04xx10^(8)dyn//cm^(2)`
Therefore, Tension`=` Tensile stress`xx` Area of cross section
`=5.04xx10^(8)xx0.005dyn`
`=25.2xx10^(5)dyh=25.2N`
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