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Alamina occupies the region inside the circle x 2  + y 2 = 4y but outside the circle x 2 + y 2 = 4. The density at each point is inversely proportional to its distance from the orgin. Where is the center of mass? The answer is attached as a photo

Alamina occupies the region inside the circle x 2  + y 2 = 4y but outside the circle x 2 + y 2 = 4. The density at each point is inversely proportional to its distance from the orgin. Where is the center of mass? The answer is attached as a photo

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Alamina occupies the region inside the circle x 2  + y 2 = 4y but outside the circle x 2 + y 2 = 4. The density at each point is inversely proportional to its distance from the orgin. Where is the center of mass?

The answer is attached as a photo

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Now mass m = SS density dA again in polar we get 2 Sino dir dodo 55/6 2 sino d dodo 55/6 2sino do 5N6 2 sin o-1 do 57/6 2 Coso 9/ + 2x 3 2 2x 3 - *3+ [ GJ3 -A m = 3 Hence centre of mass (x, Cy) = (My, m) (0, 3 = (0, ) > (0, 106 3J3 6 J3 -27 5.196 4:/ 08 8 Centre of mass (0, 1•2<46) CS$canned with CamScanner
Transcribed Image Text:Now mass m = SS density dA again in polar we get 2 Sino dir dodo 55/6 2 sino d dodo 55/6 2sino do 5N6 2 sin o-1 do 57/6 2 Coso 9/ + 2x 3 2 2x 3 - *3+ [ GJ3 -A m = 3 Hence centre of mass (x, Cy) = (My, m) (0, 3 = (0, ) > (0, 106 3J3 6 J3 -27 5.196 4:/ 08 8 Centre of mass (0, 1•2<46) CS$canned with CamScanner
Now converting it into polar r dr do so x*+ ya = 4 in polar r ² - 4 11 point of intersection is 53,1) or (r,0) = () N = TOSO, y = rsino J3 = YWSO , y - rsino = | tano = fa ) 0 = 30 %3D so r = J3 xcoS30 = 3 so point (3 ) Also (-J3,1) is , S) 2Sino rsino r dr do Hence Mx = 2 Sino Sino 2 Sine 4 Siro -1) do 5TY6 A j" (4 sin'o - Sino)do 5下(G sino - sin3 o Sino S/6 A- 2coso. t cos30 2 + x0 - 23 -0 11 2 2 6J3 213 CSScanned with CamScanner
Transcribed Image Text:Now converting it into polar r dr do so x*+ ya = 4 in polar r ² - 4 11 point of intersection is 53,1) or (r,0) = () N = TOSO, y = rsino J3 = YWSO , y - rsino = | tano = fa ) 0 = 30 %3D so r = J3 xcoS30 = 3 so point (3 ) Also (-J3,1) is , S) 2Sino rsino r dr do Hence Mx = 2 Sino Sino 2 Sine 4 Siro -1) do 5TY6 A j" (4 sin'o - Sino)do 5下(G sino - sin3 o Sino S/6 A- 2coso. t cos30 2 + x0 - 23 -0 11 2 2 6J3 213 CSScanned with CamScanner
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