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Direction: In the following question consists of two statements Assertion(A) and Reason(R). You have to read the statements carefully and select the answers to these questions using the options below.
Assertion (A): a material is incompressible if its poissions ratio is 0.5
Reason(R): the bulk modulus K is related to modulus of elasticity E and to poissons ratio as per well known relationship.
Assertion (A): a material is incompressible if its poissions ratio is 0.5
Reason(R): the bulk modulus K is related to modulus of elasticity E and to poissons ratio as per well known relationship.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true and R is not the correct explanation of A Correct Answer
- c)A is true but R is false
- d)A is false but R is true
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Direction: In the following question consists of two statements Assert...
Most materials have poissons ratio values ranging between 0 and 0.5. a perfectly incompressible material deformed elastically at small strains would have poissons ration of exactly 0.5 at this value material is incompressible.
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Direction: In the following question consists of two statements Assert...
Assertion (A): A material is incompressible if its Poisson's ratio is 0.5.
Reason (R): The bulk modulus K is related to the modulus of elasticity E and Poisson's ratio as per a well-known relationship.
Explanation:
To understand the given assertion and reason, let's break down the concepts involved:
Poisson's Ratio:
Poisson's ratio is a measure of the relative change in lateral and axial dimensions of a material when it is subjected to an external force. It is denoted by the Greek letter 'ν' (nu). Mathematically, it can be defined as the ratio of the transverse strain to the axial strain.
Incompressible Material:
An incompressible material is one that does not change its volume when subjected to an external force. In other words, for an incompressible material, the bulk modulus (K) is infinite.
Bulk Modulus:
The bulk modulus (K) is a measure of a material's resistance to uniform compression. It quantifies the change in volume per unit change in pressure. Mathematically, it can be defined as the ratio of the change in pressure to the relative change in volume.
Modulus of Elasticity:
The modulus of elasticity (E) is a measure of a material's stiffness or resistance to deformation. It quantifies the stress-strain relationship of a material. Mathematically, it can be defined as the ratio of stress to strain.
Relationship between Bulk Modulus, Modulus of Elasticity, and Poisson's Ratio:
The relationship between the bulk modulus (K), modulus of elasticity (E), and Poisson's ratio (ν) can be expressed as follows:
K = E / (3(1 - 2ν))
Here, '3(1 - 2ν)' is the term that relates the bulk modulus to the modulus of elasticity and Poisson's ratio.
Analysis of Assertion and Reason:
From the given assertion, it states that a material is incompressible if its Poisson's ratio is 0.5. This implies that if ν = 0.5, then K = E / (3(1 - 2ν)) = E / (3(1 - 2(0.5))) = E / (3(1 - 1)) = E / (3(0)) = E / 0, which means K is infinite. This aligns with the definition of an incompressible material where the bulk modulus is infinite.
The reason provided states that the bulk modulus is related to the modulus of elasticity and Poisson's ratio. This is true, as explained by the relationship mentioned earlier.
Conclusion:
Both the assertion and the reason are true, and the reason correctly explains the assertion. Hence, the correct answer is option 'B' - Both A and R are true, and R is the correct explanation of A.
Reason (R): The bulk modulus K is related to the modulus of elasticity E and Poisson's ratio as per a well-known relationship.
Explanation:
To understand the given assertion and reason, let's break down the concepts involved:
Poisson's Ratio:
Poisson's ratio is a measure of the relative change in lateral and axial dimensions of a material when it is subjected to an external force. It is denoted by the Greek letter 'ν' (nu). Mathematically, it can be defined as the ratio of the transverse strain to the axial strain.
Incompressible Material:
An incompressible material is one that does not change its volume when subjected to an external force. In other words, for an incompressible material, the bulk modulus (K) is infinite.
Bulk Modulus:
The bulk modulus (K) is a measure of a material's resistance to uniform compression. It quantifies the change in volume per unit change in pressure. Mathematically, it can be defined as the ratio of the change in pressure to the relative change in volume.
Modulus of Elasticity:
The modulus of elasticity (E) is a measure of a material's stiffness or resistance to deformation. It quantifies the stress-strain relationship of a material. Mathematically, it can be defined as the ratio of stress to strain.
Relationship between Bulk Modulus, Modulus of Elasticity, and Poisson's Ratio:
The relationship between the bulk modulus (K), modulus of elasticity (E), and Poisson's ratio (ν) can be expressed as follows:
K = E / (3(1 - 2ν))
Here, '3(1 - 2ν)' is the term that relates the bulk modulus to the modulus of elasticity and Poisson's ratio.
Analysis of Assertion and Reason:
From the given assertion, it states that a material is incompressible if its Poisson's ratio is 0.5. This implies that if ν = 0.5, then K = E / (3(1 - 2ν)) = E / (3(1 - 2(0.5))) = E / (3(1 - 1)) = E / (3(0)) = E / 0, which means K is infinite. This aligns with the definition of an incompressible material where the bulk modulus is infinite.
The reason provided states that the bulk modulus is related to the modulus of elasticity and Poisson's ratio. This is true, as explained by the relationship mentioned earlier.
Conclusion:
Both the assertion and the reason are true, and the reason correctly explains the assertion. Hence, the correct answer is option 'B' - Both A and R are true, and R is the correct explanation of A.
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Direction: In the following question consists of two statements Assertion(A) and Reason(R). You have to read the statements carefully and select the answers to these questions using the options below.Assertion (A):a material is incompressible if its poissions ratio is 0.5Reason(R):the bulk modulus K is related to modulus of elasticity E and to poissons ratio as per well known relationship.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true and R is not the correct explanation of ACorrect Answerc)A is true but R is falsed)A is false but R is trueCorrect answer is option 'B'. Can you explain this answer?
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Direction: In the following question consists of two statements Assertion(A) and Reason(R). You have to read the statements carefully and select the answers to these questions using the options below.Assertion (A):a material is incompressible if its poissions ratio is 0.5Reason(R):the bulk modulus K is related to modulus of elasticity E and to poissons ratio as per well known relationship.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true and R is not the correct explanation of ACorrect Answerc)A is true but R is falsed)A is false but R is trueCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Direction: In the following question consists of two statements Assertion(A) and Reason(R). You have to read the statements carefully and select the answers to these questions using the options below.Assertion (A):a material is incompressible if its poissions ratio is 0.5Reason(R):the bulk modulus K is related to modulus of elasticity E and to poissons ratio as per well known relationship.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true and R is not the correct explanation of ACorrect Answerc)A is true but R is falsed)A is false but R is trueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following question consists of two statements Assertion(A) and Reason(R). You have to read the statements carefully and select the answers to these questions using the options below.Assertion (A):a material is incompressible if its poissions ratio is 0.5Reason(R):the bulk modulus K is related to modulus of elasticity E and to poissons ratio as per well known relationship.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true and R is not the correct explanation of ACorrect Answerc)A is true but R is falsed)A is false but R is trueCorrect answer is option 'B'. Can you explain this answer?.
Direction: In the following question consists of two statements Assertion(A) and Reason(R). You have to read the statements carefully and select the answers to these questions using the options below.Assertion (A):a material is incompressible if its poissions ratio is 0.5Reason(R):the bulk modulus K is related to modulus of elasticity E and to poissons ratio as per well known relationship.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true and R is not the correct explanation of ACorrect Answerc)A is true but R is falsed)A is false but R is trueCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Direction: In the following question consists of two statements Assertion(A) and Reason(R). You have to read the statements carefully and select the answers to these questions using the options below.Assertion (A):a material is incompressible if its poissions ratio is 0.5Reason(R):the bulk modulus K is related to modulus of elasticity E and to poissons ratio as per well known relationship.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true and R is not the correct explanation of ACorrect Answerc)A is true but R is falsed)A is false but R is trueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following question consists of two statements Assertion(A) and Reason(R). You have to read the statements carefully and select the answers to these questions using the options below.Assertion (A):a material is incompressible if its poissions ratio is 0.5Reason(R):the bulk modulus K is related to modulus of elasticity E and to poissons ratio as per well known relationship.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true and R is not the correct explanation of ACorrect Answerc)A is true but R is falsed)A is false but R is trueCorrect answer is option 'B'. Can you explain this answer?.
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