A brass wire 1.8 m long at `27^(C)` is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of `–39^(@)C`, what is the tension developed in the wire, if its diameter is 2.0 mm ? Co-efficient of linear expansion of brass `= 2.0xx 10^(–5) K^(–1)`, Young’s modulus of brass `= 0.91xx 10^(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`