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CSIR-NET 2017 DEC 118

118. An isotropic, homogeneous sample is subjected  to uniaxial stress along the x-axis. The absolute  value of the axial strain is found to be thrice the  normal strain. The ratio (Vp/Vs) of the P wave  and S wave velocity is 

1. 1.5 

2. 1.75 

3. 2.0 

4. 2.25


Solution:
Poisson's ratio is defined as the negative of the ratio of the lateral strain to the axial strain for a uniaxial stress state.

Poisson's ratio (ν ) = \frac{normal strain}{axial strain}

From the above problem, axial strain = 3 normal strain

  
ν =\frac{1}{3}

\frac{1}{3} = \frac{normal strain}{axial strain}

The relation between velocities of P and S-waves and Poisson's ratio is given below 

\frac{V_{p}}{V_{s}} =\sqrt\frac{2(1-ν)}{(1-2ν)}  

\frac{V_{p}}{V_{s}}=\sqrt\frac{2(1-\frac{1}{3})}{(1-2*\frac{1}{3})}

\frac{V_{p}}{V_{s}} =\sqrt4

\frac{V_{p}}{V_{s}} =2





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