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 $100^o C$ is: (For steel Young's modulus is $2 \times 10^{11}$ $Nm^{-1}$ and coefficient of thermal expansion is $1.1 \times 10^{-5}$ $K^{-1}$ )
JEE MAIN 2014, Medium
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$Young's\,modulus\,Y = \frac{{stress}}{{strain}}$
$stress = Y \times strain$
$Stress\,in\,steel\,wire = Applied\,pressure$
$pressure = stress = Y \times strain$
$strain = \frac{{\Delta L}}{L} = \alpha \Delta T\left( {As\,length\,is\,constant} \right)$
$ = 2 \times {10^{11}} \times 1.1 \times {10^{ - 5}} \times 100$
$ = 2.2 \times {10^8}Pa$
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