Question

A steel wire of length $20cm$ and uniform cross section $1m{m}^2$ is tied rigidly at both the ends. If temperature of the wire is altered from $40^{\circ }C$ to $20^{\circ }C$. Calculate the change in tension. (Given coefficient of linear expansion of steel $\alpha =1.1\times 10^{-5}/{}^{\circ }C$ and Young's modulus $Y$ for steel $=2\times 10^{11}N/m^2$ )

• A. 88 N
• B. 11 N
• C. 44 N
• D. 22 N

Answer 1

Answer: (C)

The change in tension, when wire is cooled is given by
$F=yA\alpha \Delta \theta$
Given, $\Delta \theta =40^{\circ }-20^{\circ }=20^{\circ }C$,
$A=1m{m}^2=1\times 10^{-6}{m}^2,$
$\alpha =1.1\times 10^{-5}/{}^{\circ }C,$
$Y=2\times 10^{11}N/m^2$
$\therefore F=2\times 10^{11}\times 10^{-6}\times 1.1\times 10^{-5}\times 20$
$\Rightarrow F=44N$