Question

A steel rod of length $1\text{m}$ is fixed between two walls. If the rod is heated from ${25}^o\text{C}$ to ${35}^o\text{C}$, the stress developed in the rod is expressed as $x\times {10}^7{\text{N/m}}^2$. Find the value of $x$.
(coefficient of expansion for steel is $2\times {10}^{-5}{/}^{\circ }C$, Young's modulus of steel is $2\times {10}^{11}{\text{N/m}}^2$)

• A. $2$
• B. $4$
• C. $7$
• D. $8$

Answer 1

The correct option is B $4$

Due to heating the strain developed in the steel rod can be calculated as
$\frac{\Delta l}{l}=\alpha \times \Delta T$
We know
$Y=\frac{\text{stress}}{\text{strain}}$
$\text{stress}=Y\times \text{strain}$
$\text{stress}=Y\times \alpha \times \Delta T$
$\text{stress}=2\times {10}^{11}\times 2\times {10}^{-5}\times 10$
$\text{stress}=4\times {10}^7{\text{N/m}}^2$
Hence $x=4$