Question

If the temperature of a wire of length $2\text{m}$ and area of cross-section $1{\text{cm}}^2$ is increased from $0^{\circ }\text{C}$ to ${80}^{\circ }\text{C}$, then force required so that the wire is not allowed to increase in length is: (Given $Y={10}^{10}{\text{N/m}}^2,\alpha ={10}^{-6}{/}^{\circ }\text{C}$)

• A. $160\text{N}$
• B. $80\text{N}$
• C. $400\text{N}$
• D. $120\text{N}$

Answer 1

The correct option is B $80\text{N}$

We know that,
Force exerted on the supports to prevent the increase in length due to thermal expansion is given by,
$F=YA\alpha \Delta \theta$
Given, $\Delta \theta =80-0={80}^{\circ }\text{C}$
$A=1{\text{cm}}^2,\alpha ={10}^{-6}{/}^{\circ }\text{C}$
So,
$F={10}^{10}\times 0.0001\times {10}^{-6}\times 80$
$\Rightarrow F=80\text{N}$