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If E,G and K have their usual meanings, for an elastic material, then which one of the following be possibly true?
- a)G = 2K
- b)G = K
- c)K = E
- d)G = E = K
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If E,G and K have their usual meanings, for an elastic material, then ...
As E = 2G(1 + μ) = 3K(1 – 2μ) = 9KG / (3K + G)
The value of μ must be between 0 to 0.5, so as E never equal to G but if μ = 1/3, then E=K.
The value of μ must be between 0 to 0.5, so as E never equal to G but if μ = 1/3, then E=K.
Most Upvoted Answer
If E,G and K have their usual meanings, for an elastic material, then ...
Explanation:
Given Information:
- For an elastic material, the relationships between the shear modulus (G), Young's modulus (E), and bulk modulus (K) are typically defined as follows:
- G = E / (2(1 + v)), where v is Poisson's ratio
- K = E / (3(1 - 2v)), where v is Poisson's ratio
Analysis of Options:
- a) G = 2K: This is not a valid relationship for an elastic material based on the given formulas. Therefore, option a) is not true.
- b) G = K: By comparing the formulas for G and K, it is evident that G is not equal to K in general for an elastic material. Therefore, option b) is not true.
- c) K = E: By analyzing the relationship between K and E, it can be seen that K and E are not equal for an elastic material based on the given formulas. Therefore, option c) is not true.
- d) G = E = K: This relationship is not valid based on the given formulas for an elastic material. Therefore, option d) is not true.
Conclusion:
- The only possible true statement among the given options is:
- c) K = E
Therefore, the correct answer is option c) K = E.
Given Information:
- For an elastic material, the relationships between the shear modulus (G), Young's modulus (E), and bulk modulus (K) are typically defined as follows:
- G = E / (2(1 + v)), where v is Poisson's ratio
- K = E / (3(1 - 2v)), where v is Poisson's ratio
Analysis of Options:
- a) G = 2K: This is not a valid relationship for an elastic material based on the given formulas. Therefore, option a) is not true.
- b) G = K: By comparing the formulas for G and K, it is evident that G is not equal to K in general for an elastic material. Therefore, option b) is not true.
- c) K = E: By analyzing the relationship between K and E, it can be seen that K and E are not equal for an elastic material based on the given formulas. Therefore, option c) is not true.
- d) G = E = K: This relationship is not valid based on the given formulas for an elastic material. Therefore, option d) is not true.
Conclusion:
- The only possible true statement among the given options is:
- c) K = E
Therefore, the correct answer is option c) K = E.
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Question Description
If E,G and K have their usual meanings, for an elastic material, then which one of the following be possibly true?a)G = 2Kb)G = Kc)K = Ed)G = E = KCorrect 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 E,G and K have their usual meanings, for an elastic material, then which one of the following be possibly true?a)G = 2Kb)G = Kc)K = Ed)G = E = KCorrect 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 E,G and K have their usual meanings, for an elastic material, then which one of the following be possibly true?a)G = 2Kb)G = Kc)K = Ed)G = E = KCorrect answer is option 'C'. Can you explain this answer?.
If E,G and K have their usual meanings, for an elastic material, then which one of the following be possibly true?a)G = 2Kb)G = Kc)K = Ed)G = E = KCorrect 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 E,G and K have their usual meanings, for an elastic material, then which one of the following be possibly true?a)G = 2Kb)G = Kc)K = Ed)G = E = KCorrect 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 E,G and K have their usual meanings, for an elastic material, then which one of the following be possibly true?a)G = 2Kb)G = Kc)K = Ed)G = E = KCorrect answer is option 'C'. Can you explain this answer?.
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