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For this exercise we will use the fact (see Exercise 32 in Section 6.5) that the moments of a combination of regions is the sum of the moments of the individual regions. Thus in particular if R is composed of two subregions, R₁ and R₂, then y (area of R)= y₁ (area of R₁) + y₂ (area of R₂) One circle C₁ of radius 2 is centered at the origin. On top of the circle a second circle, C₂, is placed, with radius 1 and center (0, 8). Find the center of gravity, (x, y), of the combination of the two circles.

For this exercise we will use the fact (see Exercise 32 in Section 6.5) that the moments of a combination of regions is the sum of the moments of the individual regions. Thus in particular if R is composed of two subregions, R₁ and R₂, then y (area of R)= y₁ (area of R₁) + y₂ (area of R₂) One circle C₁ of radius 2 is centered at the origin. On top of the circle a second circle, C₂, is placed, with radius 1 and center (0, 8). Find the center of gravity, (x, y), of the combination of the two circles.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For this exercise we will use the fact (see Exercise 32 in Section 6.5) that the moments of a combination of regions is the sum of the moments of the individual regions. Thus in particular if R is composed of two subregions, R₁ and R₂, then y (area of R) = y₁ (area of R₁) + y₂ (area of R₂) One circle C₁ of radius 2 is centered at the origin. On top of the circle a second circle, C₂, is placed, with radius 1 and center (0, 8). Find the center of gravity, (x, y), of the combination of the two circles.
Transcribed Image Text:For this exercise we will use the fact (see Exercise 32 in Section 6.5) that the moments of a combination of regions is the sum of the moments of the individual regions. Thus in particular if R is composed of two subregions, R₁ and R₂, then y (area of R) = y₁ (area of R₁) + y₂ (area of R₂) One circle C₁ of radius 2 is centered at the origin. On top of the circle a second circle, C₂, is placed, with radius 1 and center (0, 8). Find the center of gravity, (x, y), of the combination of the two circles.
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