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JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main · Physics · Mechanical Properties of Solids

A tension of 22 ~N is applied to a copper wire of cross-sectional...

A tension of 22 N22 \mathrm{~N} is applied to a copper wire of cross-sectional area 0.02 cm20.02 \mathrm{~cm}^2 Young's modulus of copper is 1.1×1011 N/m21.1 \times 10^{11} \mathrm{~N} / \mathrm{m}^2 and Poisson's ratio 0.32 . The decrease in cross-sectional area will be

Options

  1. A1.28×10−6 cm21.28 \times 10^{-6} \mathrm{~cm}^2
  2. B1.6×10−6 cm21.6 \times 10^{-6} \mathrm{~cm}^2
  3. C2.56×10−6 cm22.56 \times 10^{-6} \mathrm{~cm}^2
  4. D0.64×10−6 cm20.64 \times 10^{-6} \mathrm{~cm}^2

Correct answer

D. 0.64×10−6 cm20.64 \times 10^{-6} \mathrm{~cm}^2

Step-by-step solution

Young's modulus of materials Y=F×lAΔl,Δll=FAY=220.02×10−4×1.1×1011=10−4Y=\frac{F \times l}{A \Delta l}, \frac{\Delta l}{l}=\frac{F}{A Y}=\frac{22}{0.02 \times 10^{-4} \times 1.1 \times 10^{11}}=10^{-4} Poisson's ratio, σ=ΔllΔrr\sigma=\frac{\frac{\Delta l}{l}}{\frac{\Delta r}{r}}Δll=σΔrr=0.32×Δrr=0.32×10−4=32×10−6\begin{aligned} \frac{\Delta l}{l} & =\sigma \frac{\Delta r}{r}=0.32 \times \frac{\Delta r}{r} \\ & =0.32 \times 10^{-4}=32 \times 10^{-6}\end{aligned}Thedecreaseincross−sectionalarea,The decrease in cross-sectional area,\begin{aligned} & \frac{\Delta A}{A}=\frac{\Delta A}{0.02}=0.32 \times \frac{\Delta l}{l} \\ & \Delta A=0.64 \times 10^{-6} \mathrm{~cm}^2\end{aligned}$$
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