Question

The Young's modulus of a material is $2\times {10}^{11}N/m^2$ and its elastic limit is $1.8\times {10}^{8}N/m^2$. For a wire of $1m$ length of this material, the maximum elongation achievable is

• A. $0.2mm$
• B. $0.3mm$
• C. $0.4mm$
• D. $0.5mm$

Answer 1

Answer: (D)

$0.5mm$

From Hooke's law $strain=\frac{stress}{Y}$
where $strain=\frac{e}{l}$
Given : $stress=1.8\times {10}^{8}N/m^2$ $Y=2\times {10}^{11}N/m^2$ $l=1m$
$\therefore$ $e=\frac{stress}{Y}l=\frac{{10}^8}{2\times {10}^{11}}\times 1=5\times {10}^{-4}m=0.5mm$