Question

A structural steel rod has a radius of $10mm$ and length of $1.0m$. A $100kN$ force stretches it along its length. Young’s modulus of structural steel is $2\times 10^{11}N{m}^{-2}$. The percentage strain is about

• A. $0.16\%$
• B. $0.32\%$
• C. $0.08\%$
• D. $0.24\%$

Answer 1

Answer: (A)

Given: $F=100kN=10^{5}N$
$Y=2\times 10^{11}N{m}^{-2}<br/>{\ell }_0=1.0m$
radius $r=10mm=10^{2}m$
From formula, $Y=\frac{Stress}{Strain}$
$\Rightarrow Strain=\frac{Stress}{Y}=\frac{F}{AY}$
$=\frac{10^5}{\pi r^{2}Y}=\frac{10^5}{3.14\times 10^{-4}\times 2\times 10^{11}}$
$=\frac{1}{628}$
Therefore % strain $=\frac{1}{628}\times 100=0.16\%$