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  • Try this! - Properties of Solids and Liquids - JEE Main-2

A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are  7.7\times 10^{3}kg/m^{3}\; and\; 2.2\times 10^{11}N/m^{2} respectively ?

 

 

  • Option 1)

    770 Hz

  • Option 2)

    188.5 Hz

  • Option 3)

    178.2 Hz

  • Option 4)

    200.5 Hz

 

Answers (1)

best_answer

As we have learned

Young Modulus -

Ratio of normal stress to longitudnal strain

it denoted by Y

Y= \frac{Normal \: stress}{longitudnal\: strain}

- wherein

Y=\frac{F/A}{\Delta l/L}

F -  applied force

A -  Area

\Delta l -  Change in lenght

l - original length

 

 

 

 Fundamental frequency 

v = \frac{1}{2l }\cdot \sqrt{\frac{T}{\mu}}= \frac{1}{2l}\sqrt{\frac{T}{\rho A}}

\frac{1}{2l }\cdot \sqrt{\frac{stress}{\rho}}= \frac{1}{2\times 1.5}\sqrt{\frac{Y\times stress}{\rho }}

\frac{1}{3 }\cdot \sqrt{\frac{2.2 \times 10^1^1\times 10^{-2}}{7.7\times 10^3}} = 178.2 Hz

 

 

 

 

 

 


Option 1)

770 Hz

Option 2)

188.5 Hz

Option 3)

178.2 Hz

Option 4)

200.5 Hz

Posted by

SudhirSol

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