A structural steel rod has a radius of 10,mm and length of 1.0,m. A 100,kN force stretches it along

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8.Mechanical Properties of Solids

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

A

$0.16$

B

$0.32$

C

$0.08$

D

$0.24$

(AIEEE-2012)

Solution

$Given:F = 100kN = {10^5}N$

$Y = 2 \times {10^{11}}N{m^{ – 2}}$

${\ell _0} = 1.0m$

$radius\,r = 10mm = {10^{ – 2}}m$

$From\,formula,\,y = \frac{{Stress}}{{Strain}}$

$ \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}}$

$Therefor\% strain = \frac{1}{{628}} \times 10 = 0.16\% $

Standard 11

Physics

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