Question

Diameter of steel rod fixed between two rigid supports is $20\text{mm}$. Find the stress in the rod when the temperature increases by ${80}^{\circ }\text{C}$.
$($Take Young's modulus, $Y=2\times {10}^{11}{\text{N/m}}^2$ and thermal expansion coefficient ,$\alpha =12\times {10}^{-6}/{}^{\circ }\text{C})$

• A. $150\text{MPa}$
• B. $192\text{MPa}$
• C. $250\text{MPa}$
• D. $100\text{MPa}$

Answer 1

The correct option is B $192\text{MPa}$

We know that,
Modulus of elasticity,
$Y=\frac{\text{Stress}}{\text{Strain}}$
$\Rightarrow \text{Stress}=Y\times \text{Strain}$ ...........(1)
Strain,
$\frac{\Delta L}{L}=\alpha \Delta T=12\times {10}^{-6}\times 80$
$=9.6\times {10}^{-4}$.........(2)

On putting value from (2) in (1), we get
$\text{Stress}=2\times {10}^{11}\times 9.6\times {10}^{-4}$
$\Rightarrow \text{Stress}=192\text{MPa}$