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  • Help me please, In materials like aluminium and copper the correct order of magnitude of various elastic modulii is :

 In materials like aluminium and copper the correct order of magnitude of various elastic modulii is :            

 

  • Option 1)

    Young’s modulii < shear modulii  < bulk modulii.       
     

     

  • Option 2)

     Bulk  modulii  <  shear  modulii  < Young’s modulii.       
         

  • Option 3)

    Shear modulii < Young’s modulii  < bulk modulii.      
     

  • Option 4)

      Bulk modulii < Young’s modulii   < shear modulii.  

 

Answers (1)

best_answer

As we have learned

Volumetri'c strain -

\frac{\Delta V}{V}

- wherein

\Delta V\rightarrow Change \: in \: volume

V\rightarrow original \: volume

 

 

Bulk Modulus -

Ratio of normal stress to volumetric strain.

K=\frac{f/A}{-\Delta v/v}=\frac{-Fv}{A\Delta v}

K=\frac{-Pv}{\Delta v}

v = Original  volume

\Delta v = Change in volume

P = Increase in pressure

-ve(sign) shows volume (\Delta v) decrease.

- wherein

 

 

Modulus of Rigidity -

G = \frac{Tangential\: stress}{shearing\: strain}

- wherein

 

 Poisson ratio \sigma = \frac{lateral \: \: strain }{longitudinal \: \: strain }

For copper 

\sigma = 0.33 \\and \: \: Y = 3k (1-2\sigma )\\also \frac{g}{Y}= \frac{1}{K}+\frac{3}{\eta }\\ Y = 2 \eta (1+ \sigma )

Hence  \eta < Y < K

Shear modulii < young modulli < bulk modulli

 

 

 

 

 

 


Option 1)

Young’s modulii < shear modulii  < bulk modulii.       
 

 

Option 2)

 Bulk  modulii  <  shear  modulii  < Young’s modulii.       
     

Option 3)

Shear modulii < Young’s modulii  < bulk modulii.      
 

Option 4)

  Bulk modulii < Young’s modulii   < shear modulii.  

Posted by

SudhirSol

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