The stress that has to be applied to the ends of a steel wire of length 20 cm to keep its length constant, when its temperature is raised by $100^{\circ} \mathrm{C}$ is $2.2 \times 10^x \mathrm{~Pa}$. The value of $x$ is $\qquad$ $\begin{aligned} & \text { (Given } Y=2 \times 10^{11} \mathrm{Nm}^{-2}, \\ & \left.\alpha=1.1 \times 10^{-5} \mathrm{C}^{-1}\right) \end{aligned}$

Solution

From Hook's law, $Y=\frac{\text { Stress }}{\text { Strain }}$
$\begin{aligned} & \therefore \quad \text { Stress }=Y \times \text { Strain } \\ & \text { Now, } \quad \text { Strain }=\frac{\Delta L}{L}=\frac{L \alpha \Delta T}{L}=\alpha \Delta T \\ & \therefore \quad \text { Stress }=Y \times \alpha \Delta T \\ & =2 \times 10^{11} \times 1.1 \times 10^{-5} \times 100 \\ & =2.2 \times 10^8 \mathrm{~Pa} \end{aligned}$
According to question, $\begin{aligned} 2.2 \times 10^x & =2.2 \times 10^8 \\ x & =8 \end{aligned}$

Hence, the correct answer is 8.