Question

A brass wire $2m$ long at $27^{\circ }C$ is held taut with negligible tension between two rigid supports. If the wire is cooled to a temperature of $-33^{\circ }C$, then the tension developed in the wire, its diameter being $2mm$, will be (coefficient of linear expansion of brass $=2.0\times 10^{-5}/{}^{\circ }C$ and Young's modulus of brass $=0.91\times 10^{11}Pa$ )

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

Answer 1

Answer: (C)

Thermal stress that is produced in an elastic wire is $Y\alpha \theta$ 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 $\times$ area of cross section
$=Y\alpha \times (\Delta T)\left[\pi r^2\right]N$
$=0.91\times 10^{11}\times 2\times 10^{-5}\times [27-(-33)]\left[\pi \times 1\times 10^{-6}\right]N$
$=0.91\times 2\times 6\times 3.14\times 10N$
$=34.4\times 10N=0.34kN$