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What is the ratio of Youngs modulus E to shear modulus G in terms of Poissons ratio?
- a)2(1 + μ)
- b)2(1 – μ)
- c)1/2 (1 – μ)
- d)1/2 (1 + μ)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What is the ratio of Youngs modulus E to shear modulus G in terms of P...
As we know G = E / 2(1 +μ) so this gives the ratio of E to G = 2(1 + μ).
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What is the ratio of Youngs modulus E to shear modulus G in terms of P...
Understanding the Relationship Between Young's Modulus, Shear Modulus, and Poisson's Ratio
To find the ratio of Young's modulus (E) to shear modulus (G) in terms of Poisson's ratio (μ), we start with the fundamental definitions and relationships in material mechanics.
Definitions
- Young's Modulus (E): A measure of the stiffness of a solid material, defined as the ratio of tensile stress to tensile strain.
- Shear Modulus (G): A measure of how a material deforms under shear stress, defined as the ratio of shear stress to shear strain.
Relationship with Poisson's Ratio
- Poisson's Ratio (μ): The ratio of lateral strain to axial strain when a material is stretched.
Formulation of the Ratio
The relationship between E, G, and μ is given by the equation:
E = 2G(1 + μ)
From this equation, we can derive the ratio of E to G:
E/G = 2(1 + μ)
This indicates that the ratio of Young's modulus to shear modulus is directly influenced by Poisson's ratio.
Revisiting the Options
Considering the options provided:
- a) 2(1 + μ) (Correct)
- b) 2(1 - μ)
- c) 1/2 (1 - μ)
- d) 1/2 (1 + μ)
The correct answer is option 'a', not 'c'.
Conclusion
The confusion may arise in interpreting the relationship; however, it is clear that the ratio of Young's modulus (E) to shear modulus (G) in terms of Poisson's ratio (μ) is indeed given by:
E/G = 2(1 + μ)
This relationship is fundamental in material science and mechanical engineering, aiding in the understanding of material behavior under various loading conditions.
To find the ratio of Young's modulus (E) to shear modulus (G) in terms of Poisson's ratio (μ), we start with the fundamental definitions and relationships in material mechanics.
Definitions
- Young's Modulus (E): A measure of the stiffness of a solid material, defined as the ratio of tensile stress to tensile strain.
- Shear Modulus (G): A measure of how a material deforms under shear stress, defined as the ratio of shear stress to shear strain.
Relationship with Poisson's Ratio
- Poisson's Ratio (μ): The ratio of lateral strain to axial strain when a material is stretched.
Formulation of the Ratio
The relationship between E, G, and μ is given by the equation:
E = 2G(1 + μ)
From this equation, we can derive the ratio of E to G:
E/G = 2(1 + μ)
This indicates that the ratio of Young's modulus to shear modulus is directly influenced by Poisson's ratio.
Revisiting the Options
Considering the options provided:
- a) 2(1 + μ) (Correct)
- b) 2(1 - μ)
- c) 1/2 (1 - μ)
- d) 1/2 (1 + μ)
The correct answer is option 'a', not 'c'.
Conclusion
The confusion may arise in interpreting the relationship; however, it is clear that the ratio of Young's modulus (E) to shear modulus (G) in terms of Poisson's ratio (μ) is indeed given by:
E/G = 2(1 + μ)
This relationship is fundamental in material science and mechanical engineering, aiding in the understanding of material behavior under various loading conditions.
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What is the ratio of Youngs modulus E to shear modulus G in terms of Poissons ratio?a)2(1 + μ)b)2(1 – μ)c)1/2 (1 – μ)d)1/2 (1 + μ)Correct answer is option 'C'. 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 What is the ratio of Youngs modulus E to shear modulus G in terms of Poissons ratio?a)2(1 + μ)b)2(1 – μ)c)1/2 (1 – μ)d)1/2 (1 + μ)Correct answer is option 'C'. 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 What is the ratio of Youngs modulus E to shear modulus G in terms of Poissons ratio?a)2(1 + μ)b)2(1 – μ)c)1/2 (1 – μ)d)1/2 (1 + μ)Correct answer is option 'C'. Can you explain this answer?.
What is the ratio of Youngs modulus E to shear modulus G in terms of Poissons ratio?a)2(1 + μ)b)2(1 – μ)c)1/2 (1 – μ)d)1/2 (1 + μ)Correct answer is option 'C'. 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 What is the ratio of Youngs modulus E to shear modulus G in terms of Poissons ratio?a)2(1 + μ)b)2(1 – μ)c)1/2 (1 – μ)d)1/2 (1 + μ)Correct answer is option 'C'. 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 What is the ratio of Youngs modulus E to shear modulus G in terms of Poissons ratio?a)2(1 + μ)b)2(1 – μ)c)1/2 (1 – μ)d)1/2 (1 + μ)Correct answer is option 'C'. Can you explain this answer?.
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