Question

A steel rod of length $1m$ and radius $10mm$ is stretched by a force $100kN$ along its length. The stress produced in the rod is then
$(Y_{steel}=2\times {10}^{11}N{m}^{-2})$

• A. $3.18\times {10}^{6}N{m}^{-2}$
• B. $3.18\times {10}^{7}N{m}^{-2}$
• C. $3.18\times {10}^{8}N{m}^{-2}$
• D. $3.18\times {10}^{9}N{m}^{-2}$

Answer 1

The correct option is C $3.18\times {10}^{8}N{m}^{-2}$

Here $r=10mm=10\times {10}^{-3}m={10}^{-2}m$
$L=1m,F=100kN=100\times {10}^{3}N={10}^{5}N$

Stress produced in the rod is:

$Stress=\frac{F}{A}=\frac{F}{\pi r^2}=\frac{100\times {10}^{3}N}{3.14\times {\left({10}^{-2}m\right)}^2}=3.18\times {10}^{8}N{m}^{-2}$