Question

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

• A. $20$
• B. $15$
• C. $10$
• D. $0$

Answer 1

Answer: (C)

$10$

Modulus of elasticity $=\frac{Force}{Area}\times \frac{l}{\Delta l}$

$3\times {10}^{11}=\frac{33000}{{10}^{-3}}\times \frac{l}{\Delta l}$

$\frac{\Delta l}{l}=\frac{33000}{{10}^{-3}}\times \frac{1}{3\times {10}^{11}}$

$=11\times {10}^{-5}$

Change in length, $\frac{\Delta l}{l}=\alpha \Delta T$
$11\times {10}^{-5}=1.1\times {10}^{-5}\times \Delta T$
$\Rightarrow \Delta T=10K$ or $10$