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For a linear elastic and isotropic material, the correct relationship among Young’s modulus of elasticity $(E)$, Poisson’s ratio $(\nu),$ and shear modulus $(G)$ is

  1. $G= \frac{E}{2(1+\nu)}$ 
  2. $G= \frac{E}{(1+2\nu)}$ 
  3. $E= \frac{G}{2(1+\nu)}$ 
  4. $E= \frac{G}{(1+2\nu)}$ 
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