Question

There is some change in length when a $33000\text{N}$ tensile force is applied on a steel rod of area of cross section ${10}^{-3}{\text{m}}^2$. The change of temperature required to produce the same elongation, if steel rod is heated, is: (The modulus of elasticity is $3\times {10}^{11}{\text{N/m}}^2$ and the coefficient of linear expansion of steel is $1.1\times {{10}^{-5}}^{\circ }{C}^{-1}$)

• A. ${10}^{\circ }C$
• B. $1^{\circ }C$
• C. ${20}^{\circ }C$
• D. ${30}^{\circ }C$

Answer 1

The correct option is A ${10}^{\circ }C$

We know ,
Modulus of elasticity, $Y=\frac{\text{Force}}{\text{Area}}\times \frac{l}{\Delta l}$
$\Rightarrow 3\times {10}^{11}=\frac{33000}{{10}^{-3}}\times \frac{l}{\Delta l}$
$\Rightarrow \frac{\Delta l}{l}=\frac{33000}{{10}^{-3}}\times \frac{1}{3\times {10}^{11}}=11\times {10}^{-5}$

Also,
Change in length (thermal strain), $\frac{\Delta l}{l}=\alpha \Delta T$
$\Rightarrow 11\times {10}^{-5}=1.1\times {10}^{-5}\times \Delta T$
$\Rightarrow \Delta T={10}^{\circ }C$