Question

If the temperature of a wire of length $2m$ and area of cross-section $1c{m}^2$ is increased from $0^{\circ }C$ to $80^{\circ }C$ and is not allowed to increase in length, then force required for it is $\left\{Y=10^{10}N/m^2,\alpha =10^{-6}/{}^{\circ }C\right\}$

• A. 80 N
• B. 160 N
• C. 400 N
• D. 120 N

Answer 1

Answer: (A)

Thermal expansion would be $=L\propto \Delta T$
Where $L=$ original length
$\alpha =$ coefficient of linear expansion
$\Delta T=$ Change in temperature
So substituting values
$\Delta L=2\times 10^{-6}\times 80$
$\Delta L=1.6\times 10^{-4}m$
Now $\Delta L=\frac{FL}{AY}$
$\frac{\Delta L\times AY}{L}=F$
Substitute values
$\frac{1.6\times 10^{-4}\times 10^{10}\times 1}{2\times 10000}=F$
$80N=F$