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JEE Main 20127 MayOnline
Exam
JEE Main
Year
2012
Date
7 May
Mode
Online
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main 2012 · 7 May · Online · Physics · Mechanical Properties of Solids

A structural steel rod has a radius of 10 ~mm and length of 1.0 ~m...

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

Options

  1. A0.16%0.16 \%
  2. B0.32%0.32 \%
  3. C0.08%0.08 \%
  4. D0.24%0.24 \%

Correct answer

A. 0.16%0.16 \%

Step-by-step solution

Given: F=100kN=105 NF=100 \mathrm{kN}=10^5 \mathrm{~N}Y=2×1011Nm−2ℓ0=1.0 m\begin{aligned}& \mathrm{Y}=2 \times10^{11} \mathrm{Nm}^{-2}\\ & \ell_0=1.0 \mathrm{~m} \end{aligned}radius $\mathrm{r}=10 \mathrm{~mm}=10^{-2} \mathrm{~m}$ From formula, $Y=\frac{\text{ Stress }}{\text{ Strain }}$ \Rightarrow \quad $\text{ Strain }=\frac{\text{ Stress }}{Y}=\frac{F}{A Y}\begin{aligned}& =\frac{10^5}{\pi r^2 Y}=\frac{10^5}{3.14 \times 10^{-4} \times 2 \times 10^{11}}\\ & =\frac{1}{628} \end{aligned}$ThereforeTherefore\%strain=1628×100=0.16%strain =\frac{1}{628} \times 100=0.16 \%
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