Question

A steel wire of uniform cross-section of $1m{m}^2$ is heated upto ${50}^{o}C$ and clamped rigidly at its ends. If temperature of wire falls to ${40}^{o}C$, change in tension in the wire is (coefficient of linear expansion of steel is $1.1\times {10}^{-5}{/}^{o}C$ and Young's modulus of elasticity of steel is $2\times {10}^{11}N/m^2$)

• A. $22N$
• B. $44N$
• C. $88N$
• D. $88\times {10}^{6}N$

Answer 1

The correct option is A $22N$

$F=YA\frac{\Delta l}{l}=YA\alpha \Delta \theta$
$=2\times {10}^{11}\times (1\times {10}^{-6})\times 1.1\times {10}^{-5}\times \left(10\right)=22N$