Q. There is some change in 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 $3 \times 10^{11}{Nm}^{- 2}$ and the coefficient of linear expansion of steel is $1.1 \times 10^{- 5}℃^{- 1}$.
A) 20$℃$
B) $15℃$
C) $10℃$
D) $0℃$
Explanation
(c) Modulus of elasticity =$\ \frac{Force}{Area} \times \frac{l}{\mathrm{\Delta}l}$
$3 \times 10^{11}\ = \frac{33000}{10^{- 3}} \times \frac{l}{\mathrm{\Delta}l}$
$\frac{\mathrm{\Delta}l}{l}\ \ \ = \frac{33000}{10^{- 3}} \times \frac{1}{3 \times 10^{11}}$
$= 11 \times 10^{- 5}$
Change in length, $\frac{\mathrm{\Delta}l}{l} = \alpha\mathrm{\Delta}T$
$11 \times 10^{- 5}$ = $1.1 \times 10^{- 5} \times \mathrm{\Delta}T$
$\Rightarrow$ $\mathrm{\Delta}T$ = 10K or 10$℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.