Question

A tensile force of magnitude $200\text{kN}$ is applied on the prismatic steel rod having radius $10\text{mm}$ and length $1\text{m}$. If Young's modulus of steel is $2\times {10}^{11}{\text{N/m}}^2$, find out the elongation in steel rod.

• A. $3.18\text{mm}$
• B. $6.36\text{mm}$
• C. $12.7\text{mm}$
• D. $13.6\text{mm}$

Answer 1

The correct option is A $3.18\text{mm}$

We know,
young modulus $\left(Y\right)=\frac{FL}{A\Delta L}$
$\Rightarrow \Delta L=\frac{FL}{AY}$
where $F=200\times {10}^3\text{N}$
$L=1\text{m}$
$A=\pi r^2$ [$\because r=10\text{mm}=0.01\text{m}$]
$=\pi (0.01{)}^2$
$=3.14\times {10}^{-4}{\text{m}}^2$
$Y=2\times {10}^{11}{\text{N/m}}^2$

$\Rightarrow \Delta L=\frac{200\times {10}^3\times 1}{3.14\times {10}^{-4}\times 2\times {10}^{11}}\text{m}$
$=3.18\times {10}^{-3}\text{m}=3.18\text{mm}$