A brass wire 2 m long at 27^oC is held taut with negligible tension between two rigid supports. If the wire is cooled to a temperature of -33^oC, then the tension developed in the wire, its diameter being mm, will be (coefficient of linear expansion of brass = 2.0 x 10^-5/^oC and Young's modulus of brass = 0.91 x 10¹¹ Pa)

Thermal stress that is produced in an elastic wire is  $\mathrm{Y\alpha } \mathrm{\theta }$ per unit area, where Y is Young's modulus, a coefficient of linear expansion and $\mathrm{\theta }$ change of temperature.
Thus, tension developed in the wire is
T = Thermal stress x area of cross section

$\begin{array}{l}=\mathrm{Y\alpha }\times \left(\mathrm{\Delta T}\right)\left[{\mathrm{\pi r}}^2\right]\mathrm{N}\\ =0.91\times {10}^{11}\times 2\times {10}^{-5}\times [27-(-33\left)\right]\left[\mathrm{\pi }\times 1\times {10}^{-6}\right]\mathrm{N}\\ =0.91\times 2\times 6\times 3.14\times 10\mathrm{N}\\ =34.4\times 10\mathrm{N}=0.34\mathrm{kN}\end{array}$