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If Poisson's ratio of a material is 0.5, then the elastic modulus for the material is
  • a)
    three times its shear modulus
  • b)
    four times its shear modulus
  • c)
    equal to its shear modulus
  • d)
    indeterminate
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If Poisson's ratio of a material is 0.5, then the elastic modulus ...
Elastic modulus = E
Shear modulus = G
E = 2G ( 1 + μ )
Given, μ= 0.5 , E = 2x1.5xG
E = 3G.
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Most Upvoted Answer
If Poisson's ratio of a material is 0.5, then the elastic modulus ...
Explanation:
Poisson's ratio (v) is defined as the negative ratio of lateral strain to longitudinal strain. It is a dimensionless quantity and its value ranges from 0 to 0.5 for most materials.

The elastic modulus (E) is a measure of a material's stiffness and is defined as the ratio of stress to strain in the linear elastic region.

The shear modulus (G) is a measure of a material's resistance to deformation by shear stress.

Relation between Poisson's ratio, elastic modulus and shear modulus can be given as:
E = 2G(1+v)

Given, Poisson's ratio (v) = 0.5
Substituting the value of Poisson's ratio in the above equation, we get:
E = 2G(1+0.5)
E = 3G

Therefore, the elastic modulus for the material is three times its shear modulus. Hence, option A is the correct answer.
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If Poisson's ratio of a material is 0.5, then the elastic modulus for the material isa)three times its shear modulusb)four times its shear modulusc)equal to its shear modulusd)indeterminateCorrect answer is option 'A'. Can you explain this answer?
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