A brass wire 2 m long at `27^@C` is held taut with negligible tension between two rigid supports. If the wire is cooled to a temperature of `-33^@C`, then the tension developed in the wire, its diameter being 2 mm, will be (coefficient of linear expansion of brass`=2.0xx10^(-5)//^(@)C` and Young's modulus of brass `=0.91xx10^(11)Pa`)

Options

A. 3400N
B. 34kN
C. 0.34kN
D. 6800N

Answer

C

Explanation

Thermal stress that is produced in an elastic wire is T `alphatheta` per unit area, where Y is Young's modulus `alpha` coefficient of linear expansion and `theta` change of temperature. Thus, tension developed in the wire is
`T=`Thermal stress`xx`area of cross section
`=Yalphaxx(DeltaT)[pir^2]N`
`=0.91xx10^11xx2xx10^-5xx[27-(-33)][pixx1xx10^-6]N`
`=0.91xx2xx6xx3.14xx10N`
`=34.4xx10N=0.34kN`