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A material having modulus of elasticity 200 GN/m2 and Poissons ratio 0.25 will have modulus of rigidity
- a)80 GN/m2
- b)120 GN/m2
- c)160 GN/m2
- d)240 GN/m2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A material having modulus of elasticity 200 GN/m2 and Poissons ratio 0...
Relation between young's modulus or Modulus of Elasticity(E), Rigidity modulus(G) and Poisson's ratio(u).
E = 2G(1+u).
=> G = E/[2(1+u)]
=> G = 200/2.5
=> G = 80 GN/m^2
Most Upvoted Answer
A material having modulus of elasticity 200 GN/m2 and Poissons ratio 0...
As we know that modulus of rigidity =E/3 , hence when you divide 200/3 ...you get 66.66...so it nearer to 80 hence option A is correct.... by this way you always get an approximate answer.... so option A is correct
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Community Answer
A material having modulus of elasticity 200 GN/m2 and Poissons ratio 0...
The Modulus of Rigidity
The modulus of rigidity, also known as shear modulus, is a measure of a material's resistance to shearing deformation. It is denoted by the symbol G and is defined as the ratio of shear stress to shear strain.
Modulus of Elasticity
The modulus of elasticity, also known as Young's modulus, is a measure of a material's stiffness or ability to resist deformation under tensile or compressive forces. It is denoted by the symbol E and is defined as the ratio of stress to strain.
Poisson's Ratio
Poisson's ratio is a measure of the relative contraction or expansion of a material in the directions perpendicular to the applied load. It is denoted by the symbol ν (nu) and is defined as the ratio of lateral strain to longitudinal strain.
Relationship between Modulus of Elasticity and Modulus of Rigidity
There is a mathematical relationship between the modulus of elasticity (E), modulus of rigidity (G), and Poisson's ratio (ν):
E = 2G(1 + ν)
This relationship holds true for isotropic materials, which have the same properties in all directions.
Given Information
Modulus of Elasticity (E) = 200 GN/m²
Poisson's Ratio (ν) = 0.25
Calculation
Using the relationship between E, G, and ν:
E = 2G(1 + ν)
We can rearrange the equation to solve for G:
G = E / (2(1 + ν))
Substituting the given values:
G = 200 GN/m² / (2(1 + 0.25))
G = 200 GN/m² / (2.5)
G = 80 GN/m²
Conclusion
Therefore, the modulus of rigidity for the given material is 80 GN/m², which corresponds to option 'A'.
The modulus of rigidity, also known as shear modulus, is a measure of a material's resistance to shearing deformation. It is denoted by the symbol G and is defined as the ratio of shear stress to shear strain.
Modulus of Elasticity
The modulus of elasticity, also known as Young's modulus, is a measure of a material's stiffness or ability to resist deformation under tensile or compressive forces. It is denoted by the symbol E and is defined as the ratio of stress to strain.
Poisson's Ratio
Poisson's ratio is a measure of the relative contraction or expansion of a material in the directions perpendicular to the applied load. It is denoted by the symbol ν (nu) and is defined as the ratio of lateral strain to longitudinal strain.
Relationship between Modulus of Elasticity and Modulus of Rigidity
There is a mathematical relationship between the modulus of elasticity (E), modulus of rigidity (G), and Poisson's ratio (ν):
E = 2G(1 + ν)
This relationship holds true for isotropic materials, which have the same properties in all directions.
Given Information
Modulus of Elasticity (E) = 200 GN/m²
Poisson's Ratio (ν) = 0.25
Calculation
Using the relationship between E, G, and ν:
E = 2G(1 + ν)
We can rearrange the equation to solve for G:
G = E / (2(1 + ν))
Substituting the given values:
G = 200 GN/m² / (2(1 + 0.25))
G = 200 GN/m² / (2.5)
G = 80 GN/m²
Conclusion
Therefore, the modulus of rigidity for the given material is 80 GN/m², which corresponds to option 'A'.
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Question Description
A material having modulus of elasticity 200 GN/m2 and Poissons ratio 0.25 will have modulus of rigiditya)80 GN/m2 b)120 GN/m2c)160 GN/m2 d)240 GN/m2Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A material having modulus of elasticity 200 GN/m2 and Poissons ratio 0.25 will have modulus of rigiditya)80 GN/m2 b)120 GN/m2c)160 GN/m2 d)240 GN/m2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A material having modulus of elasticity 200 GN/m2 and Poissons ratio 0.25 will have modulus of rigiditya)80 GN/m2 b)120 GN/m2c)160 GN/m2 d)240 GN/m2Correct answer is option 'A'. Can you explain this answer?.
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