Question

An iron rod of length $1\text{m}$ is fixed between two walls as shown in figure. Find thermal stress and thermal strain developed in the rod if it is heated by $\Delta T={20}^{\circ }C$
(Given: Coefficient of linear expansion of iron is $1.2\times {10}^{-5}{}^{\circ }{C}^{-1}$; Young's modulus of iron is $2\times {10}^{11}{\text{N/m}}^2$).

• A. $24\times {10}^7{\text{N/m}}^2,48\times {10}^{-5}$
• B. $48\times {10}^6{\text{N/m}}^2,32\times {10}^{-4}$
• C. $32\times {10}^7{\text{N/m}}^2,48\times {10}^{-4}$
• D. $48\times {10}^6{\text{N/m}}^2,24\times {10}^{-5}$

Answer 1

The correct option is D $48\times {10}^6{\text{N/m}}^2,24\times {10}^{-5}$

We know that,
Thermal strain $=\alpha \Delta T=\frac{\Delta L}{L_o}$
Where, $\alpha =$ Coefficient of linear expansion
$\Delta T=$ Change in temperature
$L_o=$ Original length
$\therefore \frac{\Delta L}{L_o}=1.2\times {10}^{-5}\times 20=24\times {10}^{-5}$

Also,
Thermal stress $=Y\alpha \Delta T$
$=2\times {10}^{11}\times 1.2\times {10}^{-5}\times 20$
$=48\times {10}^6{\text{N/m}}^2$