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Assertion (A): A long column of square cross section has greater buckling stability than a similar column of circular cross-section of same length, same material and same area of cross-section with same end conditions.
Reason (R): A circular cross-section has a smaller second moment of area than a square cross-section of same area.
- 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 'A'. Can you explain this answer?
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Assertion (A): A long column of square cross section has greater buckl...
Understanding Buckling Stability in Columns
When comparing buckling stability between different cross-sectional shapes, it is essential to consider both the geometry and the moment of inertia.
Assertion (A)
- A long column with a square cross-section indeed has greater buckling stability than a similar column with a circular cross-section, given that all other factors (length, material, area, and end conditions) are the same.
Reason (R)
- The reason behind this assertion is that a circular cross-section typically has a smaller second moment of area (also known as the area moment of inertia) compared to a square cross-section of the same area.
Key Points
- Second Moment of Area: The second moment of area is crucial in determining a column’s resistance to buckling. A higher moment indicates better stability.
- Square vs. Circular Cross-Section: For a given cross-sectional area, the square section distributes material more effectively away from the centerline, enhancing its moment of inertia compared to a circular section.
- Conclusion: Since both the assertion and reason are true, and the reason directly supports the assertion, option 'A' correctly states that R is indeed the correct explanation of A.
In summary, the geometrical properties of cross-sections play a vital role in stability, making square columns superior to circular ones in terms of buckling resistance.
When comparing buckling stability between different cross-sectional shapes, it is essential to consider both the geometry and the moment of inertia.
Assertion (A)
- A long column with a square cross-section indeed has greater buckling stability than a similar column with a circular cross-section, given that all other factors (length, material, area, and end conditions) are the same.
Reason (R)
- The reason behind this assertion is that a circular cross-section typically has a smaller second moment of area (also known as the area moment of inertia) compared to a square cross-section of the same area.
Key Points
- Second Moment of Area: The second moment of area is crucial in determining a column’s resistance to buckling. A higher moment indicates better stability.
- Square vs. Circular Cross-Section: For a given cross-sectional area, the square section distributes material more effectively away from the centerline, enhancing its moment of inertia compared to a circular section.
- Conclusion: Since both the assertion and reason are true, and the reason directly supports the assertion, option 'A' correctly states that R is indeed the correct explanation of A.
In summary, the geometrical properties of cross-sections play a vital role in stability, making square columns superior to circular ones in terms of buckling resistance.
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Assertion (A): A long column of square cross section has greater buckling stability than a similar column of circular cross-section of same length, same material and same area of cross-section with same end conditions.Reason (R): A circular cross-section has a smaller second moment of area than a square cross-section of same area.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 'A'. Can you explain this answer?
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Assertion (A): A long column of square cross section has greater buckling stability than a similar column of circular cross-section of same length, same material and same area of cross-section with same end conditions.Reason (R): A circular cross-section has a smaller second moment of area than a square cross-section of same area.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 'A'. 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): A long column of square cross section has greater buckling stability than a similar column of circular cross-section of same length, same material and same area of cross-section with same end conditions.Reason (R): A circular cross-section has a smaller second moment of area than a square cross-section of same area.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 'A'. 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): A long column of square cross section has greater buckling stability than a similar column of circular cross-section of same length, same material and same area of cross-section with same end conditions.Reason (R): A circular cross-section has a smaller second moment of area than a square cross-section of same area.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 'A'. Can you explain this answer?.
Assertion (A): A long column of square cross section has greater buckling stability than a similar column of circular cross-section of same length, same material and same area of cross-section with same end conditions.Reason (R): A circular cross-section has a smaller second moment of area than a square cross-section of same area.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 'A'. 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): A long column of square cross section has greater buckling stability than a similar column of circular cross-section of same length, same material and same area of cross-section with same end conditions.Reason (R): A circular cross-section has a smaller second moment of area than a square cross-section of same area.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 'A'. 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): A long column of square cross section has greater buckling stability than a similar column of circular cross-section of same length, same material and same area of cross-section with same end conditions.Reason (R): A circular cross-section has a smaller second moment of area than a square cross-section of same area.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 'A'. Can you explain this answer?.
Solutions for Assertion (A): A long column of square cross section has greater buckling stability than a similar column of circular cross-section of same length, same material and same area of cross-section with same end conditions.Reason (R): A circular cross-section has a smaller second moment of area than a square cross-section of same area.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 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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ample number of questions to practice Assertion (A): A long column of square cross section has greater buckling stability than a similar column of circular cross-section of same length, same material and same area of cross-section with same end conditions.Reason (R): A circular cross-section has a smaller second moment of area than a square cross-section of same area.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 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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