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If the Young’s modulus E is equal to bulk modulus K, then the value of Poisson’s ratio is
- a)1/4
- b)1/2
- c)1/3
- d)3/4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the Young’s modulus E is equal to bulk modulus K, then the va...
E = 3 K ( 1 - 2 v)
(∴ E = K)
(∴ E = K)Most Upvoted Answer
If the Young’s modulus E is equal to bulk modulus K, then the va...
Understanding Young’s Modulus and Bulk Modulus
Young’s modulus (E) and bulk modulus (K) are crucial material properties used in mechanical engineering to describe how materials deform under stress.
Definitions
- Young’s Modulus (E): Measures the tensile or compressive stiffness of a material, defined as the ratio of stress (force per unit area) to strain (proportional deformation).
- Bulk Modulus (K): Measures a material's response to uniform compression, defined as the ratio of volumetric stress to the change in volume strain.
Relationship Among Material Properties
To understand the relationship between E, K, and Poisson's ratio (ν), we can use the following formula:
- K = E / [3(1 - 2ν)]
When E = K, we can substitute K in the equation:
- E = E / [3(1 - 2ν)]
This simplifies to:
- 1 = 1 / [3(1 - 2ν)]
Solving for Poisson’s Ratio
Rearranging the equation gives:
- 3(1 - 2ν) = 1
- 1 - 2ν = 1/3
Now, solving for ν:
- 2ν = 1 - 1/3
- 2ν = 2/3
- ν = 1/3
Conclusion
Thus, when Young’s modulus equals bulk modulus, the value of Poisson’s ratio is 1/3.
Correct Answer
- The correct answer to the question is option C: 1/3.
Young’s modulus (E) and bulk modulus (K) are crucial material properties used in mechanical engineering to describe how materials deform under stress.
Definitions
- Young’s Modulus (E): Measures the tensile or compressive stiffness of a material, defined as the ratio of stress (force per unit area) to strain (proportional deformation).
- Bulk Modulus (K): Measures a material's response to uniform compression, defined as the ratio of volumetric stress to the change in volume strain.
Relationship Among Material Properties
To understand the relationship between E, K, and Poisson's ratio (ν), we can use the following formula:
- K = E / [3(1 - 2ν)]
When E = K, we can substitute K in the equation:
- E = E / [3(1 - 2ν)]
This simplifies to:
- 1 = 1 / [3(1 - 2ν)]
Solving for Poisson’s Ratio
Rearranging the equation gives:
- 3(1 - 2ν) = 1
- 1 - 2ν = 1/3
Now, solving for ν:
- 2ν = 1 - 1/3
- 2ν = 2/3
- ν = 1/3
Conclusion
Thus, when Young’s modulus equals bulk modulus, the value of Poisson’s ratio is 1/3.
Correct Answer
- The correct answer to the question is option C: 1/3.
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If the Young’s modulus E is equal to bulk modulus K, then the value of Poisson’s ratio isa)1/4b)1/2c)1/3d)3/4Correct 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 If the Young’s modulus E is equal to bulk modulus K, then the value of Poisson’s ratio isa)1/4b)1/2c)1/3d)3/4Correct 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 If the Young’s modulus E is equal to bulk modulus K, then the value of Poisson’s ratio isa)1/4b)1/2c)1/3d)3/4Correct answer is option 'C'. Can you explain this answer?.
If the Young’s modulus E is equal to bulk modulus K, then the value of Poisson’s ratio isa)1/4b)1/2c)1/3d)3/4Correct 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 If the Young’s modulus E is equal to bulk modulus K, then the value of Poisson’s ratio isa)1/4b)1/2c)1/3d)3/4Correct 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 If the Young’s modulus E is equal to bulk modulus K, then the value of Poisson’s ratio isa)1/4b)1/2c)1/3d)3/4Correct answer is option 'C'. Can you explain this answer?.
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