Question

A structural steel rod has a radius of 10 mm and a length of 1 m. A 100 kN force stretches it along its length. The strain on the rod is
$(Y_{steel}=200\times 10^{9}N{m}^{-2})$

• A. 1.6 mm
• B. 2.6 mm
• C. 3.6 mm
• D. 4.6 mm

Answer 1

Answer: (A)

Here, $r=10mm=10\times 10^{-3}m$
$L=1m$
$F=100kN=100\times 10^{3}N=10^{5}N$
Stress on the rod is given by
Stress $=\frac{F}{A}=\frac{F}{\pi r^2}$
$=\frac{100\times 10^{3}N}{3.14\times {\left(10^{-2}m\right)}^2}=3.18\times 10^{8}N{m}^{-2}$
Elongation,
$\Delta L=\frac{\left(F/A\right)L}{Y}=\frac{\left(3.18\times 10^{8}N{m}^{-2}\right)\left(1m\right)}{2\times 10^{11}N{m}^{-2}}$
$=1.59\times 10^{-3}m=1.59mm$
The strain on the rod is given by
Strain $=\frac{\Delta L}{L}$
$=\frac{1.59\times 10^{-3}m}{1m}=1.59\times 10^{-3}m=1.59mm$
$=1.6mm$