Question

A steel wire of cross-sectional area $0.5m{m}^2$ is held between two fixed supports. If the wire is just taut at ${20}^{\circ }C$, determine the tension when the temperature falls to $0^{\circ }C$. Coefficient of linear expansion of steel is $1.2\times {10}^{-5}{/}^{\circ }C$ and its Young's modulus is $2.0\times {10}^{11}N/m^2$.

• A. $24N$
• B. $12N$
• C. $4.8N$
• D. $2.4N$

Answer 1

Answer: (A)

$24N$

Here final length is more than original length so that strain is tensile and Tension is given by,

$Area\times Y\times strain=AY\alpha \Delta \theta$

Where $Y=2.0\times {10}^{11}N/m^2$ is the Young's modulus.

$\theta =20$, $\alpha =1.2\times {10}^{-5}/{}^{o}C$ is the Coefficient of thermal expansion.

$A=0.5\times {10}^{-6}{m}^2$ is the area of cross-section.

From above values, Tension is $24N$