Question

There is some change $W$ length when a $ 33000 \, N$ 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} /^{\circ} C)$.

• A. $20^{\circ} C $
• B. $15^{\circ} C $
• C. $10^{\circ} C $
• D. $0^{\circ} C $

Answer 1

Answer: (C)

Modulus of elasticity
$=\frac{\text { Force }}{\text { Area }} \times \frac{l}{\Delta l}$
$3 \times 10^{11}=\frac{33000}{10^{-3}} \times \frac{l}{\Delta l}$
$\frac{\Delta l}{l}=\frac{33000}{10^{-3}} \times \frac{1}{3 \times 10^{11}}$
$=11 \times 10^{-5}$
Change in length, $\frac{\Delta l}{l}=\alpha \Delta T$
$11 \times 10^{-5}=1.1 \times 10^{-5} \times \Delta T$
$\Rightarrow \Delta T=10\, K$ or $10^{\circ} C$