Question

There is some change in length when a 33000N tensile force is applied on a steel rod of the area of cross section ${10}^{-3}{m}^2$. The change in 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 coefficient of linear expansion of steel is $1.1\times {10}^{-5}0C^{-1}$)

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

Answer 1

The correct option is C ${10}^{0}C$

For elongation

$Y=\frac{F}{A}\frac{L}{\Delta L}3\times {10}^{11}=\frac{33000\times {10}^3}{1}\times \frac{L}{\Delta L}=\frac{\Delta L}{L}=\frac{33\times {10}^3\times {10}^3}{3\times {10}^{11}}=\frac{11}{{10}^5}\to \left(1\right)$

For exansion

$\Delta L=\alpha \Delta \theta l\frac{\Delta L}{L}=\frac{11}{{10}^6}\times \Delta \theta \to \left(2\right)$

Equating $\left(1\right)\&\left(2\right)\frac{\pi }{{10}^6}\times \Delta \theta =\frac{\pi }{{10}^5}\Delta \theta =10°C$