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A brass wire 1.8 m long at 27^(@)C is he...

A brass wire `1.8 m` long at `27^(@)C` is held taut with little tension between two rigid supports. If the wire cooled to a temperature of `-39^(@)C`, what is the tension developed in the wire, if its diameter is `2.0 mm`? Coefficient of linear expansion of brass `= 2.0 xx 10^(-5)//^(@)C`, Young's modulus of brass `= 0.91 xx 10^(11) Pa`.

A

`3.8xx10^(2)N`

B

`5.8xx10^(2)N`

C

`7.8xx10^(2)N`

D

`6.8xx10^(2)N`

Text Solution

Verified by Experts

The correct Answer is:
A
Decrease in length due to tention ltbRgt `Deltal=(Fl)/(AY)----(1)`
Increase in length due to rise in temperature `Deltall=lalphaDeltat----(2)`
from `(1)` and `(2)(Fl)/(AY)=lalphaDeltatimpliesF=YAalphaDeltaT`
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