There is some change in length when a $33000 \mathrm{~N}$ tensile force is applied on a steel rod of area of cross-section $10^{-3} \mathrm{~m}^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is $3 imes 10^{11}…

Question

There is some change in length when a $33000 \mathrm{~N}$ tensile force is applied on a steel rod of area of cross-section $10^{-3} \mathrm{~m}^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is $3 	imes 10^{11} \mathrm{~N} / \mathrm{m}^2$ and the coefficient of linear expansion of steel is $\left.1.1 	imes 10^{-5} /{ }^{\circ} \mathrm{C}ight)$.

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Modulus of elasticity }=\frac{	ext { Force }}{	ext { Area }} 	imes \frac{l}{\Delta l} \ & \qquad \begin{aligned} 3 	imes 10^{11} & =\frac{33000}{10^{-3}} 	imes \frac{l}{\Delta l} \ \frac{\Delta l}{l} & =\frac{33000}{10^{-3}} 	imes \frac{1}{3 	imes 10^{11}} \ & =11 	imes 10^{-5}\end{aligned}\end{aligned}$ Change in length, $\frac{\Delta l}{l}=\alpha \Delta T$ $ \begin{aligned} 11 	imes 10^{-5} & =1.1 	imes 10^{-5} 	imes \Delta T \ \Rightarrow \quad \Delta T & =10 \mathrm{~K} 	ext { or } 10^{\circ} \mathrm{C} \end{aligned} $

There is some change in length when a $33000 \mathrm{~N}$ tensile force is applied on a steel rod of area of…

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