Question

The pressure that has to be applied to the ends of a steel wire of length $10cm$ to keep its length constant when its temperature is raised by 100${}^o$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

We have change in length due to the change in temperature (considering no obstruction)
$\Delta L=\alpha L\Delta T$
or
$\Delta L=1.1\times {10}^{-5}\times 0.10\times 100=1.1\times {10}^{-4}m$
Now pressure which needs to be applied would be given using
$\frac{F}{A}=Pressure=\frac{\Delta L\times Y}{L}=\frac{1.1\times {10}^{-4}\times 2\times {10}^{11}}{0.1}$
(Here $\Delta L$ is the expansion prevented)
$=2.2\times {10}^{8}Pa$