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The theorem of Pappus and Guldinus states that the area of the revolving curve is ______________
- a)Product of the area, length of generated curve and the radius vector
- b)Product of the area, length of generated curve and the perpendicular distance from axis
- c)Product of the volume, length of generated curve and the radius vector
- d)Product of the volume, length of generated curve and the perpendicular distance from axis
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The theorem of Pappus and Guldinus states that the area of the revolvi...
The theorem is used to find the surface area and the volume of the revolving body. This is done by using simple integration. Thus the surface area and the volume of any 2D curve. It is just the product of the area, length of generated curve and the perpendicular distance from axis.
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The theorem of Pappus and Guldinus states that the area of the revolvi...
Understanding the Theorem of Pappus and Guldinus
The theorem of Pappus and Guldinus provides a powerful method for calculating the area and volume of surfaces generated by revolving curves about an axis. The theorem can be applied in various fields, including mechanical engineering.
Key Concepts of the Theorem
- The theorem consists of two parts: one for area and one for volume.
Area of the Revolving Curve
- The area \( A \) of the surface generated by revolving a plane curve about an external axis is given by the formula:
\[ A = L \cdot d \]
where:
- \( L \) is the length of the curve.
- \( d \) is the perpendicular distance from the axis of rotation to the centroid of the area being revolved.
Why Option B is Correct
- The correct answer is option 'B': **Product of the area, length of generated curve and the perpendicular distance from axis** because:
- It emphasizes the importance of the **perpendicular distance** from the axis, which is crucial in determining how far the area is from the axis of rotation.
- The formula effectively combines the area of the shape being revolved with the distance from the axis to yield the area of the surface generated.
Volume of the Revolving Curve
- Similarly, the volume \( V \) generated by revolving a solid about an external axis is calculated using:
\[ V = A \cdot d \]
where \( A \) is the area of the shape and \( d \) is the distance from the axis of rotation to the centroid.
Conclusion
Understanding the theorem of Pappus and Guldinus is essential for calculating areas and volumes in mechanical engineering applications, allowing for efficient design and analysis of components.
The theorem of Pappus and Guldinus provides a powerful method for calculating the area and volume of surfaces generated by revolving curves about an axis. The theorem can be applied in various fields, including mechanical engineering.
Key Concepts of the Theorem
- The theorem consists of two parts: one for area and one for volume.
Area of the Revolving Curve
- The area \( A \) of the surface generated by revolving a plane curve about an external axis is given by the formula:
\[ A = L \cdot d \]
where:
- \( L \) is the length of the curve.
- \( d \) is the perpendicular distance from the axis of rotation to the centroid of the area being revolved.
Why Option B is Correct
- The correct answer is option 'B': **Product of the area, length of generated curve and the perpendicular distance from axis** because:
- It emphasizes the importance of the **perpendicular distance** from the axis, which is crucial in determining how far the area is from the axis of rotation.
- The formula effectively combines the area of the shape being revolved with the distance from the axis to yield the area of the surface generated.
Volume of the Revolving Curve
- Similarly, the volume \( V \) generated by revolving a solid about an external axis is calculated using:
\[ V = A \cdot d \]
where \( A \) is the area of the shape and \( d \) is the distance from the axis of rotation to the centroid.
Conclusion
Understanding the theorem of Pappus and Guldinus is essential for calculating areas and volumes in mechanical engineering applications, allowing for efficient design and analysis of components.
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The theorem of Pappus and Guldinus states that the area of the revolving curve is ______________a)Product of the area, length of generated curve and the radius vectorb)Product of the area, length of generated curve and the perpendicular distance from axisc)Product of the volume, length of generated curve and the radius vectord)Product of the volume, length of generated curve and the perpendicular distance from axisCorrect answer is option 'B'. Can you explain this answer?
Question Description
The theorem of Pappus and Guldinus states that the area of the revolving curve is ______________a)Product of the area, length of generated curve and the radius vectorb)Product of the area, length of generated curve and the perpendicular distance from axisc)Product of the volume, length of generated curve and the radius vectord)Product of the volume, length of generated curve and the perpendicular distance from axisCorrect answer is option 'B'. 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 The theorem of Pappus and Guldinus states that the area of the revolving curve is ______________a)Product of the area, length of generated curve and the radius vectorb)Product of the area, length of generated curve and the perpendicular distance from axisc)Product of the volume, length of generated curve and the radius vectord)Product of the volume, length of generated curve and the perpendicular distance from axisCorrect answer is option 'B'. 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 The theorem of Pappus and Guldinus states that the area of the revolving curve is ______________a)Product of the area, length of generated curve and the radius vectorb)Product of the area, length of generated curve and the perpendicular distance from axisc)Product of the volume, length of generated curve and the radius vectord)Product of the volume, length of generated curve and the perpendicular distance from axisCorrect answer is option 'B'. Can you explain this answer?.
The theorem of Pappus and Guldinus states that the area of the revolving curve is ______________a)Product of the area, length of generated curve and the radius vectorb)Product of the area, length of generated curve and the perpendicular distance from axisc)Product of the volume, length of generated curve and the radius vectord)Product of the volume, length of generated curve and the perpendicular distance from axisCorrect answer is option 'B'. 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 The theorem of Pappus and Guldinus states that the area of the revolving curve is ______________a)Product of the area, length of generated curve and the radius vectorb)Product of the area, length of generated curve and the perpendicular distance from axisc)Product of the volume, length of generated curve and the radius vectord)Product of the volume, length of generated curve and the perpendicular distance from axisCorrect answer is option 'B'. 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 The theorem of Pappus and Guldinus states that the area of the revolving curve is ______________a)Product of the area, length of generated curve and the radius vectorb)Product of the area, length of generated curve and the perpendicular distance from axisc)Product of the volume, length of generated curve and the radius vectord)Product of the volume, length of generated curve and the perpendicular distance from axisCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The theorem of Pappus and Guldinus states that the area of the revolving curve is ______________a)Product of the area, length of generated curve and the radius vectorb)Product of the area, length of generated curve and the perpendicular distance from axisc)Product of the volume, length of generated curve and the radius vectord)Product of the volume, length of generated curve and the perpendicular distance from axisCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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