## anonymous one year ago INTEGRATION The inner and outer radii of a half hollow sphere are a and b.Find the center of gravity.Please help

1. anonymous

Through intergration

2. anonymous

You have to consider this as a solid sphere and then integrate from a to b right?

3. anonymous

You have to consider this as a solid sphere and then integrate from a to b right?

4. geerky42

Can you help? @ganeshie8 @zepdrix

5. anonymous

I know the answer but don't know how to prove

6. Elsa213
7. anonymous

Nope

8. zepdrix

center of gravity? .... wh... ut? 0_o

9. geerky42

Nothing to do with moment of inertia lol

10. geerky42

I think it's best that you define for us exactly what "center of gravity" is. @Zupari

11. geerky42

Looks more like question for physicist, not mathematician lol.

12. anonymous

Sorry i don't know the exact english word but i think thats the word

13. anonymous

Centre of gravity of a hollow sphere is a/2 likewise you have to integrate and find the point of this object

14. zepdrix

the translation is fine :) im just not familiar with the concept. hmm

15. ganeshie8

is it a complete sphere or an hemisphere ?

16. anonymous

hemishpere

17. ganeshie8

because if it were a complete sphere, dont u think the center of gravity just lies at the center

18. ganeshie8

ohk..

19. geerky42

Complete sphere would be more trivial, but he still have to prove it either way.

20. anonymous

answer is 3{(a+b)(a^2 + b^2)}/8( a^2 + ab + b^2)

21. ganeshie8

do you mean (0, 0, 3{(a+b)(a^2 + b^2)}/8( a^2 + ab + b^2))

22. anonymous

i think so

23. anonymous

https://www.youtube.com/watch?v=UiAH-Ev6PRA watch this if u don't know the concept.

24. anonymous

likewise you have to apply that to this boy.

25. anonymous

dont know how but i

26. anonymous

yoda

27. dan815

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28. anonymous

yep

29. dan815

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30. anonymous

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31. dan815

oh thats beautiful

32. dan815

i like this simplification, just find it for 2 circles

33. dan815

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34. anonymous

i cant get the given answer

35. dan815

by symmetry the center x is the origin now just determine y center

36. anonymous

its not that simple you have to integrate

37. dan815

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38. dan815

can you think of how to write that with integration

39. dan815

or u can try to find the mean radius too that is fine

40. dan815

i am thinking of this one geometrical way, maybe it works maybe it doesnt take al ook at it

41. dan815

how about finding a point such that the sum of all the vectors from the edge will equal 0

42. dan815

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43. anonymous

$\int\limits_{a}^bb ^{2}x - x ^{3}/\int\limits_{a}^b a ^{2} - x ^{2}$

44. anonymous

by solving this i dont get the given answer

45. dan815

find this out though because there might be a really nice way if u get this

46. dan815

cause then you can take the mean of the 2 given radii (a+b)/2 and see what the point on that circle radius would be such that all the sum of the vectors = 0

47. anonymous

honestly i don't know what u just said maybe its because we are 100s of miles away and our education system is different

48. dan815

49. anonymous

im in sri lanka if u've heard

50. dan815

yes ofcourse

51. anonymous

cool

52. dan815

okay wait, so how did u get those 2 integrals

53. dan815

$\int\limits_{a}^bb ^{2}x - x ^{3}/\int\limits_{a}^b a ^{2} - x ^{2}$

54. anonymous

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55. anonymous

m for mass

56. anonymous

p for density

57. dan815

okay

58. dan815

well we can ignore that since we are assume its homogenous, we are finding center of volume, but continue

59. anonymous

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60. dan815

ok yes

61. anonymous

since the solid part is from a to b integral is from a to b BUT I CANT GET THE ANSWER

62. dan815

okay try this

63. dan815

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64. dan815

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65. dan815

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66. dan815

does this make sense? we are finding the mean height

67. anonymous

uhhh...i dont know how to solve that square root inside integral our syllabus doesn;t include that part

68. anonymous

oh wait

69. dan815

ya u have to convert to polar coord

70. dan815

here is a better way from polar

71. dan815

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72. anonymous

just forget it

73. dan815

wait why dont give up

74. dan815

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75. dan815

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76. dan815

solve that integral

77. dan815

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78. dan815

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