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Assertion(A): Poisson’s ratio of a material is a measure of its ductility
Reason(R): For every linear strain in the direction of force, Poisson’s ratio of the material gives the lateral strain in directions perpendicular to the direction of force
- a)Both A and R are individually true and R is the correct explanation of A
- b)Both A and R are individually true but R is not the correct explanation of A
- c)A is true but R is false
- d)A is false but R is true
Correct answer is option 'D'. Can you explain this answer?
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Assertion(A): Poisson’s ratio of a material is a measure of its ducti...
Assertion (A): Poisson’s ratio of a material is a measure of its ductility.
Reason (R): For every linear strain in the direction of force, Poisson’s ratio of the material gives the lateral strain in directions perpendicular to the direction of force.
The correct answer is option 'D', which states that Assertion (A) is false but Reason (R) is true.
Explanation:
- Assertion (A): Poisson’s ratio of a material is a measure of its ductility.
- Reason (R): For every linear strain in the direction of force, Poisson’s ratio of the material gives the lateral strain in directions perpendicular to the direction of force.
Let's analyze both the assertion and the reason in detail:
Assertion (A): Poisson’s ratio of a material is a measure of its ductility.
- Poisson's ratio is a measure of the ratio of lateral strain to the linear strain in a material when it is subjected to an external force or stress. It is denoted by the Greek letter ν (nu).
- Ductility, on the other hand, is a measure of a material's ability to deform under tensile stress without fracture. It is a property that determines the extent to which a material can be stretched or deformed before it breaks.
- While both Poisson's ratio and ductility are related to the deformation behavior of a material, they are not directly interchangeable. Poisson's ratio specifically quantifies the relationship between linear and lateral strain, while ductility refers to the material's ability to undergo plastic deformation without fracture.
- Therefore, assertion (A) is false.
Reason (R): For every linear strain in the direction of force, Poisson’s ratio of the material gives the lateral strain in directions perpendicular to the direction of force.
- The reason provided is true. Poisson's ratio is defined as the negative ratio of the lateral strain to the linear strain in a material. Mathematically, it can be expressed as:
ν = - (lateral strain / linear strain)
- When a material is subjected to an external force or stress, it undergoes deformation. This deformation can result in both linear strain in the direction of force and lateral strain in directions perpendicular to the force.
- Poisson's ratio quantifies the relationship between these strains. It provides a measure of how much a material expands or contracts in directions perpendicular to the applied force when it is stretched or compressed in the direction of the force.
- Therefore, reason (R) is true.
In conclusion, while reason (R) is true, assertion (A) is false because Poisson's ratio is not a direct measure of a material's ductility.
Reason (R): For every linear strain in the direction of force, Poisson’s ratio of the material gives the lateral strain in directions perpendicular to the direction of force.
The correct answer is option 'D', which states that Assertion (A) is false but Reason (R) is true.
Explanation:
- Assertion (A): Poisson’s ratio of a material is a measure of its ductility.
- Reason (R): For every linear strain in the direction of force, Poisson’s ratio of the material gives the lateral strain in directions perpendicular to the direction of force.
Let's analyze both the assertion and the reason in detail:
Assertion (A): Poisson’s ratio of a material is a measure of its ductility.
- Poisson's ratio is a measure of the ratio of lateral strain to the linear strain in a material when it is subjected to an external force or stress. It is denoted by the Greek letter ν (nu).
- Ductility, on the other hand, is a measure of a material's ability to deform under tensile stress without fracture. It is a property that determines the extent to which a material can be stretched or deformed before it breaks.
- While both Poisson's ratio and ductility are related to the deformation behavior of a material, they are not directly interchangeable. Poisson's ratio specifically quantifies the relationship between linear and lateral strain, while ductility refers to the material's ability to undergo plastic deformation without fracture.
- Therefore, assertion (A) is false.
Reason (R): For every linear strain in the direction of force, Poisson’s ratio of the material gives the lateral strain in directions perpendicular to the direction of force.
- The reason provided is true. Poisson's ratio is defined as the negative ratio of the lateral strain to the linear strain in a material. Mathematically, it can be expressed as:
ν = - (lateral strain / linear strain)
- When a material is subjected to an external force or stress, it undergoes deformation. This deformation can result in both linear strain in the direction of force and lateral strain in directions perpendicular to the force.
- Poisson's ratio quantifies the relationship between these strains. It provides a measure of how much a material expands or contracts in directions perpendicular to the applied force when it is stretched or compressed in the direction of the force.
- Therefore, reason (R) is true.
In conclusion, while reason (R) is true, assertion (A) is false because Poisson's ratio is not a direct measure of a material's ductility.
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Assertion(A): Poisson’s ratio of a material is a measure of its ductilityReason(R): For every linear strain in the direction of force, Poisson’s ratio of the material gives the lateral strain in directions perpendicular to the direction of forcea) Both A and R are individually true and R is the correct explanation of Ab) Both A and R are individually true but R is not the correct explanation of Ac) A is true but R is falsed) A is false but R is trueCorrect answer is option 'D'. Can you explain this answer?
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ample number of questions to practice Assertion(A): Poisson’s ratio of a material is a measure of its ductilityReason(R): For every linear strain in the direction of force, Poisson’s ratio of the material gives the lateral strain in directions perpendicular to the direction of forcea) Both A and R are individually true and R is the correct explanation of Ab) Both A and R are individually true but R is not the correct explanation of Ac) A is true but R is falsed) A is false but R is trueCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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