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  • Speed of transverse wave of a straight wire (mass=6.0 g, length=60 cm and area of cross-section=1.0 mm2) is 90 ms-1. If the young's modulus of wire is 

Speed of transverse wave of a straight wire (mass=6.0 g, length=60 cm and area of cross-section=1.0 mm2) is 90 ms-1. If the young's modulus of wire is 16\times10^{11} Nm^{-2}, the extension of wire over its natural length is:
 
Option: 1 0.03 \: mm
Option: 2 0.04 \: mm
Option: 3 0.02\: mm  
Option: 4 0.01 \: mm
 

Answers (1)

best_answer

 

 

Hooke’s law -

Hooke’s law states that if the deformation is small, the stress in a body is proportional to the corresponding strain, i.e.,

Stress\ \alpha \ Strain 

\Rightarrow Stress=E(Strain)

\Rightarrow E=\frac{Stress}{Strain}

Where E is called as Modulus of elasticity and it depends on the nature of the material and temperature of the body and is independent of the dimensions of the body.

Unit of Modulus of elasticity= N/m2

Young's Modulus(Y):- It is defined as the ratio of longitudinal stress to longitudinal strain.

Y=\frac{longitudinal\ stress}{longitudinal\ strain}=\frac{F/A}{\Delta L/L}=\frac{Fl}{A\Delta L}

 

The linear mass density 

\\\mu=\frac{m}{l}=\frac{6\times10^{-3}}{60\times10^{-2}}\\=10^{-2}Kgm^{-1}\\given\ v=90ms^{-1}\\v=\sqrt{\frac{T}{\mu}}\\T=\mu v^2=81N\\Youngs\ modulus\\Y=\frac{\frac{F}{A}}{\frac{\Delta l}{l}}

\\\Delta l=\frac{FL}{AY}=\frac{81\times0.6}{10^{-6}\times16\times10^{11}}=0.03mm

So option (1) is correct.

Posted by

Ritika Jonwal

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