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GATE 2022 CE (CE2) – Question 13

Solid Mechanics · Simple stress and strain relationships · 1 mark · Multiple choice

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

  1. $G=E/[2(1+\nu)]$
  2. $G=E/(1+2\nu)$
  3. $E=G/[2(1+\nu)]$
  4. $E=G/(1+2\nu)$

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Show answer and explanation

Correct answer: (A) $G=E/[2(1+\nu)]$

Explanation

For isotropic linear elasticity, $E=2G(1+\nu)$. Rearranging gives $G=E/[2(1+\nu)]$.

Thus **A** is correct. The alternatives interchange E and G or use the wrong Poisson-ratio factor.