Question

The pressure that has to be applied to the ends of a steel wire of length $10$ cm to keep its length constant when its temperature is raised by ${100}^{\circ }C$ is : (For steel Young's modulus is $2\times {10}^{11}N{m}^{-2}$ and coefficient of thermal expansion is $1.1\times {10}^{-5}{K}^{-1}$)

• A. $2.2\times {10}^{7}Pa$
• B. $2.2\times {10}^{6}Pa$
• C. $2.2\times {10}^{8}Pa$
• D. $2.2\times {10}^{9}Pa$

Answer 1

The correct option is C $2.2\times {10}^{8}Pa$

Given,

$\Delta T={100}^{0}C$

$\alpha =1.1\times {10}^{-5}{/}^{0}C$

$Y=2\times {10}^{11}N/m$

In thermal expansion,

$\frac{\Delta l}{l}=\alpha \Delta T$

$\frac{\Delta l}{l}=1.1\times {10}^{-5}\times 100=1.1\times {10}^{-3}$

Pressure, $P=Y\frac{\Delta l}{l}$

$P=2\times {10}^{11}\times 1.1\times {10}^{-3}$

$P=2.2\times {10}^{8}Pa$

The correct option is C.