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The Poisson ratio of a material which has Young's modulus of 120 GPa and shear modulus of 50GPa, is
- a)0.1
- b)0.2
- c)0.3
- d)0.4
Correct answer is option 'B'. Can you explain this answer?
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The Poisson ratio of a material which has Youngs modulus of 120 GPa an...
Young's Modulus and Shear Modulus
Young's modulus (E) is a material property that measures its stiffness or ability to resist deformation in the axial direction (along the length). Shear modulus (G) measures a material's resistance to deformation in the perpendicular directions (transverse or shear deformation).
Given values:
Young's modulus (E) = 120 GPa
Shear modulus (G) = 50 GPa
The Poisson Ratio
The Poisson ratio (ν) is a measure of the ratio of lateral strain (strain perpendicular to the applied force) to axial strain (strain parallel to the applied force) in a material. It is denoted by the Greek letter ν (nu).
Mathematically, the Poisson ratio is given by the equation:
ν = (lateral strain) / (axial strain)
or
ν = - (transverse strain) / (axial strain)
Relationship between Poisson ratio, Young's modulus, and Shear modulus
The Poisson ratio is related to Young's modulus and shear modulus through the following equation:
ν = (E - 2G) / (2G)
Solving for the Poisson ratio:
ν = (120 GPa - 2 * 50 GPa) / (2 * 50 GPa)
ν = 20 GPa / 100 GPa
ν = 0.2
Therefore, the Poisson ratio of the material is 0.2, which corresponds to option B.
Young's modulus (E) is a material property that measures its stiffness or ability to resist deformation in the axial direction (along the length). Shear modulus (G) measures a material's resistance to deformation in the perpendicular directions (transverse or shear deformation).
Given values:
Young's modulus (E) = 120 GPa
Shear modulus (G) = 50 GPa
The Poisson Ratio
The Poisson ratio (ν) is a measure of the ratio of lateral strain (strain perpendicular to the applied force) to axial strain (strain parallel to the applied force) in a material. It is denoted by the Greek letter ν (nu).
Mathematically, the Poisson ratio is given by the equation:
ν = (lateral strain) / (axial strain)
or
ν = - (transverse strain) / (axial strain)
Relationship between Poisson ratio, Young's modulus, and Shear modulus
The Poisson ratio is related to Young's modulus and shear modulus through the following equation:
ν = (E - 2G) / (2G)
Solving for the Poisson ratio:
ν = (120 GPa - 2 * 50 GPa) / (2 * 50 GPa)
ν = 20 GPa / 100 GPa
ν = 0.2
Therefore, the Poisson ratio of the material is 0.2, which corresponds to option B.
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Community Answer
The Poisson ratio of a material which has Youngs modulus of 120 GPa an...
120=2*50(1+poisson)
Poisson=0.20
Poisson=0.20
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The Poisson ratio of a material which has Youngs modulus of 120 GPa and shear modulus of 50GPa, isa)0.1b)0.2c)0.3d)0.4Correct answer is option 'B'. Can you explain this answer?
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