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Assertion (A): For a ductile material stress-strain curve is a straight line up to the yield point.
Reason (R): The material follows Hooke's law up to the point of proportionality.
- 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): For a ductile material stress-strain curve is a straigh...
Assertion (A): For a ductile material stress-strain curve is a straight line up to the yield point.
Reason (R): The material follows Hooke's law up to the point of proportionality.
The correct answer is option 'D': A is false but R is true.
Explanation:
The stress-strain curve for a ductile material typically consists of several distinct regions, including the elastic region, yield point, plastic region, and fracture point. Let's examine each of these regions to understand why option 'D' is the correct answer.
1. Elastic Region:
In the elastic region, the material behaves elastically, meaning that it returns to its original shape once the applied load is removed. This region follows Hooke's law, which states that stress is directly proportional to strain within the elastic limit. The stress-strain curve in this region is a straight line.
2. Yield Point:
Once the applied stress exceeds a certain threshold known as the yield point, the material starts to deform plastically. In this region, the material undergoes permanent deformation even after the load is removed. The stress-strain curve in this region is not a straight line; it exhibits a slight deviation from linearity.
3. Plastic Region:
After the yield point, the material enters the plastic region, where it deforms plastically without any increase in stress. The stress-strain curve in this region is typically nonlinear and exhibits strain hardening.
4. Fracture Point:
At the fracture point, the material fails and fractures. This point corresponds to the ultimate tensile strength of the material.
Explanation of the Assertion and Reason:
The reason (R) is true because up to the point of proportionality (within the elastic region), the material follows Hooke's law, and the stress-strain curve is a straight line. However, the assertion (A) is false because the stress-strain curve is not a straight line up to the yield point. The deviation from linearity at the yield point indicates the transition from elastic to plastic deformation.
Therefore, although the reason is correct, it does not provide a correct explanation for the assertion. Hence, option 'D' is the correct answer.
Reason (R): The material follows Hooke's law up to the point of proportionality.
The correct answer is option 'D': A is false but R is true.
Explanation:
The stress-strain curve for a ductile material typically consists of several distinct regions, including the elastic region, yield point, plastic region, and fracture point. Let's examine each of these regions to understand why option 'D' is the correct answer.
1. Elastic Region:
In the elastic region, the material behaves elastically, meaning that it returns to its original shape once the applied load is removed. This region follows Hooke's law, which states that stress is directly proportional to strain within the elastic limit. The stress-strain curve in this region is a straight line.
2. Yield Point:
Once the applied stress exceeds a certain threshold known as the yield point, the material starts to deform plastically. In this region, the material undergoes permanent deformation even after the load is removed. The stress-strain curve in this region is not a straight line; it exhibits a slight deviation from linearity.
3. Plastic Region:
After the yield point, the material enters the plastic region, where it deforms plastically without any increase in stress. The stress-strain curve in this region is typically nonlinear and exhibits strain hardening.
4. Fracture Point:
At the fracture point, the material fails and fractures. This point corresponds to the ultimate tensile strength of the material.
Explanation of the Assertion and Reason:
The reason (R) is true because up to the point of proportionality (within the elastic region), the material follows Hooke's law, and the stress-strain curve is a straight line. However, the assertion (A) is false because the stress-strain curve is not a straight line up to the yield point. The deviation from linearity at the yield point indicates the transition from elastic to plastic deformation.
Therefore, although the reason is correct, it does not provide a correct explanation for the assertion. Hence, option 'D' is the correct answer.
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Assertion (A): For a ductile material stress-strain curve is a straight line up to the yield point.Reason (R): The material follows Hooke's law up to the point of proportionality.a)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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Assertion (A): For a ductile material stress-strain curve is a straight line up to the yield point.Reason (R): The material follows Hooke's law up to the point of proportionality.a)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? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Assertion (A): For a ductile material stress-strain curve is a straight line up to the yield point.Reason (R): The material follows Hooke's law up to the point of proportionality.a)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? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): For a ductile material stress-strain curve is a straight line up to the yield point.Reason (R): The material follows Hooke's law up to the point of proportionality.a)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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