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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

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  1. anonymous
    • one year ago
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    Through intergration

  2. anonymous
    • one year ago
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    You have to consider this as a solid sphere and then integrate from a to b right?

  3. anonymous
    • one year ago
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    You have to consider this as a solid sphere and then integrate from a to b right?

  4. geerky42
    • one year ago
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    Can you help? @ganeshie8 @zepdrix

  5. anonymous
    • one year ago
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    I know the answer but don't know how to prove

  6. Elsa213
    • one year ago
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    This might help, Zupari. c: http://physics.stackexchange.com/questions/100444/why-is-the-moment-of-inertia-for-a-hollow-sphere-higher-than-a-uniform-sphere

  7. anonymous
    • one year ago
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    Nope

  8. zepdrix
    • one year ago
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    center of gravity? .... wh... ut? 0_o

  9. geerky42
    • one year ago
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    Nothing to do with moment of inertia lol

  10. geerky42
    • one year ago
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    I think it's best that you define for us exactly what "center of gravity" is. @Zupari

  11. geerky42
    • one year ago
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    Looks more like question for physicist, not mathematician lol.

  12. anonymous
    • one year ago
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    Sorry i don't know the exact english word but i think thats the word

  13. anonymous
    • one year ago
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    Centre of gravity of a hollow sphere is a/2 likewise you have to integrate and find the point of this object

  14. zepdrix
    • one year ago
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    the translation is fine :) im just not familiar with the concept. hmm

  15. ganeshie8
    • one year ago
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    is it a complete sphere or an hemisphere ?

  16. anonymous
    • one year ago
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    hemishpere

  17. ganeshie8
    • one year ago
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    because if it were a complete sphere, dont u think the center of gravity just lies at the center

  18. ganeshie8
    • one year ago
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    ohk..

  19. geerky42
    • one year ago
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    Complete sphere would be more trivial, but he still have to prove it either way.

  20. anonymous
    • one year ago
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    answer is 3{(a+b)(a^2 + b^2)}/8( a^2 + ab + b^2)

  21. ganeshie8
    • one year ago
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    do you mean (0, 0, 3{(a+b)(a^2 + b^2)}/8( a^2 + ab + b^2))

  22. anonymous
    • one year ago
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    i think so

  23. anonymous
    • one year ago
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    https://www.youtube.com/watch?v=UiAH-Ev6PRA watch this if u don't know the concept.

  24. anonymous
    • one year ago
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    likewise you have to apply that to this boy.

  25. anonymous
    • one year ago
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    dont know how but i

  26. anonymous
    • one year ago
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    yoda

  27. dan815
    • one year ago
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    |dw:1436562405371:dw|

  28. anonymous
    • one year ago
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    yep

  29. dan815
    • one year ago
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    |dw:1436562485331:dw|

  30. anonymous
    • one year ago
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    |dw:1436562465745:dw|

  31. dan815
    • one year ago
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    oh thats beautiful

  32. dan815
    • one year ago
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    i like this simplification, just find it for 2 circles

  33. dan815
    • one year ago
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    |dw:1436562542334:dw|

  34. anonymous
    • one year ago
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    i cant get the given answer

  35. dan815
    • one year ago
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    by symmetry the center x is the origin now just determine y center

  36. anonymous
    • one year ago
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    its not that simple you have to integrate

  37. dan815
    • one year ago
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    |dw:1436562726374:dw|

  38. dan815
    • one year ago
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    can you think of how to write that with integration

  39. dan815
    • one year ago
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    or u can try to find the mean radius too that is fine

  40. dan815
    • one year ago
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    i am thinking of this one geometrical way, maybe it works maybe it doesnt take al ook at it

  41. dan815
    • one year ago
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    how about finding a point such that the sum of all the vectors from the edge will equal 0

  42. dan815
    • one year ago
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    |dw:1436562918280:dw|

  43. anonymous
    • one year ago
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    \[\int\limits_{a}^bb ^{2}x - x ^{3}/\int\limits_{a}^b a ^{2} - x ^{2}\]

  44. anonymous
    • one year ago
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    by solving this i dont get the given answer

  45. dan815
    • one year ago
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    find this out though because there might be a really nice way if u get this

  46. dan815
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    im in canada

  49. anonymous
    • one year ago
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    im in sri lanka if u've heard

  50. dan815
    • one year ago
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    yes ofcourse

  51. anonymous
    • one year ago
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    cool

  52. dan815
    • one year ago
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    okay wait, so how did u get those 2 integrals

  53. dan815
    • one year ago
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    \[ \int\limits_{a}^bb ^{2}x - x ^{3}/\int\limits_{a}^b a ^{2} - x ^{2} \]

  54. anonymous
    • one year ago
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    |dw:1436563494387:dw|

  55. anonymous
    • one year ago
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    m for mass

  56. anonymous
    • one year ago
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    p for density

  57. dan815
    • one year ago
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    okay

  58. dan815
    • one year ago
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    well we can ignore that since we are assume its homogenous, we are finding center of volume, but continue

  59. anonymous
    • one year ago
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    |dw:1436563681149:dw|

  60. dan815
    • one year ago
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    ok yes

  61. anonymous
    • one year ago
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    since the solid part is from a to b integral is from a to b BUT I CANT GET THE ANSWER

  62. dan815
    • one year ago
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    okay try this

  63. dan815
    • one year ago
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    |dw:1436563948647:dw|

  64. dan815
    • one year ago
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    |dw:1436564233941:dw|

  65. dan815
    • one year ago
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    |dw:1436564253565:dw|

  66. dan815
    • one year ago
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    does this make sense? we are finding the mean height

  67. anonymous
    • one year ago
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    uhhh...i dont know how to solve that square root inside integral our syllabus doesn;t include that part

  68. anonymous
    • one year ago
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    oh wait

  69. dan815
    • one year ago
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    ya u have to convert to polar coord

  70. dan815
    • one year ago
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    here is a better way from polar

  71. dan815
    • one year ago
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    |dw:1436564634557:dw|

  72. anonymous
    • one year ago
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    just forget it

  73. dan815
    • one year ago
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    wait why dont give up

  74. dan815
    • one year ago
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    |dw:1436565276032:dw|

  75. dan815
    • one year ago
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    |dw:1436565312287:dw|

  76. dan815
    • one year ago
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    solve that integral

  77. dan815
    • one year ago
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    |dw:1436565419033:dw|

  78. dan815
    • one year ago
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    |dw:1436565521848:dw|

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