Mechanical Properties of Solids

JEE Main level, single correct, medium

82 of 118

Question 82 of 118

A structural steel rod has a radius of 10 mm10 \mathrm{~mm} and length of 1.0 m1.0 \mathrm{~m}. A 100kN100 \mathrm{kN} force stretches it along its length. Young's modulus of structural steel is 2×1011Nm−22 \times 10^{11} \mathrm{Nm}^{-2}. The percentage strain is about

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Answer: (A) 0.16%0.16 \%

Given: F=100kN=105 NF=100 \mathrm{kN}=10^5 \mathrm{~N}
Y=2×1011Nm−2ℓ0=1.0 m\begin{aligned} & \mathrm{Y}=2 \times 10^{11} \mathrm{Nm}^{-2} \\ & \ell_0=1.0 \mathrm{~m} \end{aligned}
radius r=10 mm=10−2 m\mathrm{r}=10 \mathrm{~mm}=10^{-2} \mathrm{~m}
From formula, Y= Stress  Strain Y=\frac{\text { Stress }}{\text { Strain }}
⇒ Strain = Stress Y=FAY\Rightarrow \quad \text { Strain }=\frac{\text { Stress }}{Y}=\frac{F}{A Y}
=105πr2Y=1053.14×10−4×2×1011=1628\begin{aligned} & =\frac{10^5}{\pi r^2 Y}=\frac{10^5}{3.14 \times 10^{-4} \times 2 \times 10^{11}} \\ & =\frac{1}{628} \end{aligned}
Therefore %\% strain =1628×100=0.16%=\frac{1}{628} \times 100=0.16 \%

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