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Explain PAPPUS theorem to find Centre Of Mass of a body.

Explain PAPPUS theorem to find Centre Of Mass of a body.

Grade:12

1 Answers

Saurabh Kumar
askIITians Faculty 2400 Points
9 years ago
Pappus’ First Theorem: 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, or it’s center of mass In mathematical notation,

Usually, we know the surface area of a surface of revolution generated by the revolution of a curve about a given external axis, the arc length which are together sufficient to calculate the center of mass, by using the equation above.

Just to get a feel of it, here’s an example which illustrates the simplicity of the theorem:
Pappus’ Second Theorem: The second theorem of Pappus states that the volume of a solid of revolution generated by the revolution of a lamina about an external axis is equal to the product of the area of the lamina and the distance traveled by the lamina’s geometric centroid In mathematical notation,

Well, just as in the case of the first theorem, here’s an example to illustrate the simplicity of the theorem, and advantage o’er cumbersome integrals:

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