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What will be the value of the Poisson’s ratio if the Youngs modulus E is equal to the bulk modulus K?
- a)1/2
- b)1/4
- c)1/3
- d)3/4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What will be the value of the Poisson’s ratio if the Youngs modu...
K = E / 3(1 – 2μ)
Since K = E
So (1-2μ) = 1/3
Therefore, μ = 1/3.
Since K = E
So (1-2μ) = 1/3
Therefore, μ = 1/3.
Most Upvoted Answer
What will be the value of the Poisson’s ratio if the Youngs modu...
Understanding Poisson's Ratio
Poisson's ratio (ν) is a measure of the lateral strain to axial strain in materials when they are deformed elastically. It is defined as:
- ν = - (lateral strain) / (axial strain)
This ratio helps in understanding the relationship between different elastic moduli, specifically Young's modulus (E), Bulk modulus (K), and Shear modulus (G).
Relation Between Elastic Moduli
The relationship between the moduli is given by the following equations:
- E = 3K(1 - 2ν)
- K = E / (3(1 - 2ν))
When E is equal to K, we can set them equal and derive the value of Poisson's ratio.
Deriving Poisson's Ratio when E = K
1. Set E = K in the equation:
- K = 3K(1 - 2ν) / 3(1 - 2ν)
2. Simplifying the equation, we have:
- 1 = 3(1 - 2ν)
3. Rearranging gives:
- 3 - 6ν = 1
- 6ν = 2
- ν = 2 / 6 = 1 / 3
Conclusion
Thus, if the Young's modulus E is equal to the bulk modulus K, the value of Poisson's ratio (ν) is 1/3. Therefore, the correct answer is option 'C'.
This relationship is crucial in material science and engineering, as it helps predict how materials will behave under various loading conditions.
Poisson's ratio (ν) is a measure of the lateral strain to axial strain in materials when they are deformed elastically. It is defined as:
- ν = - (lateral strain) / (axial strain)
This ratio helps in understanding the relationship between different elastic moduli, specifically Young's modulus (E), Bulk modulus (K), and Shear modulus (G).
Relation Between Elastic Moduli
The relationship between the moduli is given by the following equations:
- E = 3K(1 - 2ν)
- K = E / (3(1 - 2ν))
When E is equal to K, we can set them equal and derive the value of Poisson's ratio.
Deriving Poisson's Ratio when E = K
1. Set E = K in the equation:
- K = 3K(1 - 2ν) / 3(1 - 2ν)
2. Simplifying the equation, we have:
- 1 = 3(1 - 2ν)
3. Rearranging gives:
- 3 - 6ν = 1
- 6ν = 2
- ν = 2 / 6 = 1 / 3
Conclusion
Thus, if the Young's modulus E is equal to the bulk modulus K, the value of Poisson's ratio (ν) is 1/3. Therefore, the correct answer is option 'C'.
This relationship is crucial in material science and engineering, as it helps predict how materials will behave under various loading conditions.
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What will be the value of the Poisson’s ratio if the Youngs modulus E is equal to the bulk modulus K?a)1/2b)1/4c)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 What will be the value of the Poisson’s ratio if the Youngs modulus E is equal to the bulk modulus K?a)1/2b)1/4c)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 What will be the value of the Poisson’s ratio if the Youngs modulus E is equal to the bulk modulus K?a)1/2b)1/4c)1/3d)3/4Correct answer is option 'C'. Can you explain this answer?.
What will be the value of the Poisson’s ratio if the Youngs modulus E is equal to the bulk modulus K?a)1/2b)1/4c)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 What will be the value of the Poisson’s ratio if the Youngs modulus E is equal to the bulk modulus K?a)1/2b)1/4c)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 What will be the value of the Poisson’s ratio if the Youngs modulus E is equal to the bulk modulus K?a)1/2b)1/4c)1/3d)3/4Correct answer is option 'C'. Can you explain this answer?.
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