Question

A metal bar of $10mm$ diameter when subjected to a pull of $23.5kN$ gave an elongation of $0.3mm$ on a gauge length of $200mm$. The Young's modulus of elasticity of the metal will nearly be

• A. $200kN/m{m}^2$
• B. $300kN/m{m}^2$
• C. $360kN/m{m}^2$
• D. $400kN/m{m}^2$

Answer 1

The correct option is A $200kN/m{m}^2$


$\Delta l=0.3mm$
$\Rightarrow \epsilon =\frac{\Delta l}{l}=\frac{0.3}{200}$
$\Rightarrow \sigma =\frac{P}{A}=\epsilon E$
$\Rightarrow \frac{23.5\times {10}^3}{\pi /4\times {10}^2}=\frac{2.3}{200}\times E$
$\Rightarrow E=\frac{235}{0.785}\times \frac{200}{0.3}$
$\simeq 200\times {10}^{3}N/m{m}^2$
$\Rightarrow E=200kN/m{m}^2$