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A steel wire of length 0.20m and uniform...

A steel wire of length 0.20m and uniform cross section `10^(-6)m^(2)` is tied rigidly at both ends. The temperature of the wire is changed from `40^(@)` C to `20^(@)C`. Calculate the thermal tension in the wire given `alpha =1.1. xx 10^(-5)//.^(@)C` and `Y=2xx10^(11)Nm^(-2)`

Text Solution

Verified by Experts

Given `l=0.20m`
`A=10^(-6)m^(2)`
`theta_(2)-theta_(1)=40^(@)-20^(@)-20^(@)C" " alpha=1.1xx10^(-5)//.^(@)C` and `Y=2xx10^(11)Nm^(-2)`
We know that `alpha=(Delta l)/(l Delta theta)`
`:.Delta l=(alpha)(l Delta theta)`
So that `Y=(Fl)/(A Deltal)` may be written as
`F=Y A alpha (theta_(2)-theta_(1))`
i.e. `f=2xx10^(11)xx10^(-6)xx1.1xx10^(-5)xx20`
`F=44N`
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