Mechanical Engineering Exam > Mechanical Engineering Questions > Select the WRONG statements:a)A beam of unifo...
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Select the WRONG statements:
- a)A beam of uniform strength will have varying cross-section.
- b)I section beams are most economical.
- c)For a beam subjected to pure bending, the stress intensity in any fibre is proportional to the distance of the fibre from the neutral axis.
- d)The moment of inertia of any area is always least with respect to its radius of gyration.
Correct answer is option 'D'. Can you explain this answer?
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Select the WRONG statements:a)A beam of uniform strength will have var...
The moment of inertia of any area is always least with repsectto its center axis (not w.r.t radius of gyration).
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Select the WRONG statements:a)A beam of uniform strength will have var...
Explanation:
The correct answer is option 'D': The moment of inertia of any area is always least with respect to its radius of gyration.
Here's a detailed explanation:
1. Definition of Moment of Inertia:
The moment of inertia of an area is a property that describes the distribution of its mass or cross-sectional area around an axis. It quantifies an object's resistance to rotational motion around that axis.
2. Definition of Radius of Gyration:
The radius of gyration is a measure of how the mass or area of an object is distributed around an axis. It is defined as the square root of the ratio of the moment of inertia to the total mass or area.
3. Relationship between Moment of Inertia and Radius of Gyration:
The moment of inertia of any area can be calculated with respect to any axis passing through its centroid. The radius of gyration is then calculated by taking the square root of the moment of inertia divided by the total area.
4. Minimum Moment of Inertia with Respect to Radius of Gyration:
When considering the moment of inertia with respect to different axes, the moment of inertia is minimum when calculated with respect to the axis passing through the centroid of the area. This is a fundamental property of moment of inertia.
5. Relationship between Moment of Inertia and Cross-Sectional Shape:
The moment of inertia depends on the shape of the cross-section. Different cross-sectional shapes have different formulas for calculating the moment of inertia. For example, the moment of inertia of a rectangular cross-section is different from that of a circular cross-section.
6. Relationship between Cross-Sectional Shape and Radius of Gyration:
The radius of gyration is a geometric property that is independent of the cross-sectional shape. It only depends on the moment of inertia and the total mass or area. Therefore, the radius of gyration is the same regardless of the shape of the cross-section.
7. Why option 'D' is incorrect:
The statement in option 'D' is incorrect because the moment of inertia of any area is not always least with respect to its radius of gyration. The moment of inertia is minimum when calculated with respect to the axis passing through the centroid of the area, not with respect to the radius of gyration.
In conclusion, the statement in option 'D' is the incorrect statement among the given options. The moment of inertia of any area is not always least with respect to its radius of gyration.
The correct answer is option 'D': The moment of inertia of any area is always least with respect to its radius of gyration.
Here's a detailed explanation:
1. Definition of Moment of Inertia:
The moment of inertia of an area is a property that describes the distribution of its mass or cross-sectional area around an axis. It quantifies an object's resistance to rotational motion around that axis.
2. Definition of Radius of Gyration:
The radius of gyration is a measure of how the mass or area of an object is distributed around an axis. It is defined as the square root of the ratio of the moment of inertia to the total mass or area.
3. Relationship between Moment of Inertia and Radius of Gyration:
The moment of inertia of any area can be calculated with respect to any axis passing through its centroid. The radius of gyration is then calculated by taking the square root of the moment of inertia divided by the total area.
4. Minimum Moment of Inertia with Respect to Radius of Gyration:
When considering the moment of inertia with respect to different axes, the moment of inertia is minimum when calculated with respect to the axis passing through the centroid of the area. This is a fundamental property of moment of inertia.
5. Relationship between Moment of Inertia and Cross-Sectional Shape:
The moment of inertia depends on the shape of the cross-section. Different cross-sectional shapes have different formulas for calculating the moment of inertia. For example, the moment of inertia of a rectangular cross-section is different from that of a circular cross-section.
6. Relationship between Cross-Sectional Shape and Radius of Gyration:
The radius of gyration is a geometric property that is independent of the cross-sectional shape. It only depends on the moment of inertia and the total mass or area. Therefore, the radius of gyration is the same regardless of the shape of the cross-section.
7. Why option 'D' is incorrect:
The statement in option 'D' is incorrect because the moment of inertia of any area is not always least with respect to its radius of gyration. The moment of inertia is minimum when calculated with respect to the axis passing through the centroid of the area, not with respect to the radius of gyration.
In conclusion, the statement in option 'D' is the incorrect statement among the given options. The moment of inertia of any area is not always least with respect to its radius of gyration.
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Select the WRONG statements:a)A beam of uniform strength will have varying cross-section.b)I section beams are most economical.c)For a beam subjected to pure bending, the stress intensity in any fibre is proportional to the distance of the fibre from the neutral axis.d)The moment of inertia of any area is always least with respect to its radius of gyration.Correct answer is option 'D'. Can you explain this answer?
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Select the WRONG statements:a)A beam of uniform strength will have varying cross-section.b)I section beams are most economical.c)For a beam subjected to pure bending, the stress intensity in any fibre is proportional to the distance of the fibre from the neutral axis.d)The moment of inertia of any area is always least with respect to its radius of gyration.Correct 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 Select the WRONG statements:a)A beam of uniform strength will have varying cross-section.b)I section beams are most economical.c)For a beam subjected to pure bending, the stress intensity in any fibre is proportional to the distance of the fibre from the neutral axis.d)The moment of inertia of any area is always least with respect to its radius of gyration.Correct 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 Select the WRONG statements:a)A beam of uniform strength will have varying cross-section.b)I section beams are most economical.c)For a beam subjected to pure bending, the stress intensity in any fibre is proportional to the distance of the fibre from the neutral axis.d)The moment of inertia of any area is always least with respect to its radius of gyration.Correct answer is option 'D'. Can you explain this answer?.
Select the WRONG statements:a)A beam of uniform strength will have varying cross-section.b)I section beams are most economical.c)For a beam subjected to pure bending, the stress intensity in any fibre is proportional to the distance of the fibre from the neutral axis.d)The moment of inertia of any area is always least with respect to its radius of gyration.Correct 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 Select the WRONG statements:a)A beam of uniform strength will have varying cross-section.b)I section beams are most economical.c)For a beam subjected to pure bending, the stress intensity in any fibre is proportional to the distance of the fibre from the neutral axis.d)The moment of inertia of any area is always least with respect to its radius of gyration.Correct 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 Select the WRONG statements:a)A beam of uniform strength will have varying cross-section.b)I section beams are most economical.c)For a beam subjected to pure bending, the stress intensity in any fibre is proportional to the distance of the fibre from the neutral axis.d)The moment of inertia of any area is always least with respect to its radius of gyration.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Select the WRONG statements:a)A beam of uniform strength will have varying cross-section.b)I section beams are most economical.c)For a beam subjected to pure bending, the stress intensity in any fibre is proportional to the distance of the fibre from the neutral axis.d)The moment of inertia of any area is always least with respect to its radius of gyration.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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Select the WRONG statements:a)A beam of uniform strength will have varying cross-section.b)I section beams are most economical.c)For a beam subjected to pure bending, the stress intensity in any fibre is proportional to the distance of the fibre from the neutral axis.d)The moment of inertia of any area is always least with respect to its radius of gyration.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Select the WRONG statements:a)A beam of uniform strength will have varying cross-section.b)I section beams are most economical.c)For a beam subjected to pure bending, the stress intensity in any fibre is proportional to the distance of the fibre from the neutral axis.d)The moment of inertia of any area is always least with respect to its radius of gyration.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Select the WRONG statements:a)A beam of uniform strength will have varying cross-section.b)I section beams are most economical.c)For a beam subjected to pure bending, the stress intensity in any fibre is proportional to the distance of the fibre from the neutral axis.d)The moment of inertia of any area is always least with respect to its radius of gyration.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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