This set of Engineering Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Theorem of Pappus and Guldinus”. Explanation: The theorem is used to find the surface area and the volume of the revolving body . ... Thus the surface area and the volume of any 2D curve.
What is first theorem of Pappus Guldinus?
The Pappus–Guldin Theorems Suppose that a plane curve is rotated about an axis external to the curve . Then 1. the resulting surface area of revolution is equal to the product of the length of the curve and the displacement of its centroid; 2.
What is Pappus theorem used for?
Theorem of Pappus lets us find volume using the centroid and an integral . where V is the volume of the three-dimensional object, A is the area of the two-dimensional figure being revolved, and d is the distance traveled by the centroid of the two-dimensional figure.
What is Pappus theorem mechanics?
The first theorem of Pappus states that the surface area of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of the arc length of the generating curve and the distance traveled by the curve’s geometric centroid , (Kern and Bland 1948, pp. 110-111).
Who invented Pappus Theorem?
In mathematics, Pappus’s centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus’s theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. The theorems are attributed to Pappus of Alexandria and Paul Guldin .
How do you prove Pappus Theorem?
Let three points A, B, C be incident to a single straight line and another three points a,b,c incident to (generally speaking) another straight line. Then three pairwise intersections 1 = Bc∩bC , 2 = Ac∩aC, and 3 = Ab∩aB are incident to a (third) straight line.
What is volume Theorem?
If the top and bottom bases of a solid are equal in area , lie in parallel planes, and every section of the solid parallel to the bases is equal in area to that of the base, then the volume of the solid is the product of base and altitude.
What is created by revolution of a circle about an axis lying in its plane?
The body generated by the revolution of a plane area, about a fixed line lying in its own plane, is called a solid of revolution . ... The section of a solid of revolution by a plane, perpendicular to the axis of revolution, is a circle having its center on the axis of revolution.
What is meant by centroid?
centroid. / (ˈsɛntrɔɪd) / noun. the centre of mass of an object of uniform density , esp of a geometric figure. (of a finite set) the point whose coordinates are the mean values of the coordinates of the points of the set.
Is the distance through which its centroid was moved?
Its centroid is at a distance 12lsinα from the y axis. Rotate the line through 360 o about the y axis. The distance moved by the centroid is 2π×12lsinα=πlsinα .
What is the Pappus problem?
Unlike the geometrical problems that occupied Descartes’ early researches, the Pappus problem is a locus problem , i.e., a problem whose solution requires constructing a curve—the “Pappus curve” according to Bos’s terminology—that includes all the points that satisfy the relationship stated in the problem.
What is Pappus in plants?
The pappus is the modified calyx, the part of an individual floret , that surrounds the base of the corolla tube in flower heads of the plant family Asteraceae. ... In species such as Dandelion or Eupatorium, feathery bristles of the pappus function as a “parachute” which enables the seed to be carried by the wind.
Who was Euclidean geometry named after?
| Euclid | Known for Euclidean geometry Euclid’s Elements Euclidean algorithm | Scientific career | Fields Mathematics |
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What is centroid of a triangle?
The centroid of a triangle is the point where the three medians coincide . The centroid theorem states that the centroid is 23 of the distance from each vertex to the midpoint of the opposite side.
Where does the centroid of any triangle fall?
Where is the Centroid of Any Given Triangle Located? Centroid is the intersection of the medians of a triangle . If we construct the medians of a triangle, the point where the medians intersect is the centroid of the triangle. It is located inside the triangle.
