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Cutting a hollow sphere into 2 piece but not in half

  1. Oct 16, 2011 #1
    1. The problem statement, all variables and given/known data
    A uniform sphere of radius R is cut into two portions. The smaller portion S has height h measured from its flat surface, where h<R.

    (a) Locate the center of mass of S from its flat surface

    (b) Use (a) the locate the centre of mass of a hollow H which has the same shape and same size as S. The hollow has only a thin curved surface and without any flat surface.
    (c) Obtain the result of (b) by direct integration.
    2. Relevant equations
    This question use 2 tricks to find the center of mass of a hollow.
    1. Use substraction to substract a big object by a smaller one and then take limit. (I hope you understand what I mean.)
    2. Use direction integration.


    3. The attempt at a solution
    My answer in part b doesn't agree with part c, can anyone help me to check what happen?
     

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  3. Oct 16, 2011 #2

    vela

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    I found a different expression for the mass of the cap:
    [tex]m=\frac{\rho\pi h^2(3R-h)}{3}[/tex]
     
  4. Oct 16, 2011 #3
    In fact I have same expression as you
    [itex]\frac{h^{3}}{3}[/itex]-[itex]h^{2}R[/itex]

    But when I copy it form messy worksheet to a much neat writting, I try to simplfy the expression in my mind, unforunately, I fail:tongue2:

    So my expression for the mass is also correct.
     
    Last edited: Oct 17, 2011
  5. Oct 16, 2011 #4

    vela

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    Did you get it to work out?
     
  6. Oct 16, 2011 #5
    Yes, of course.
    I do this question with 2 other classmates, we check a hundred time for our answer. I am sure we get it correct.
     
  7. Oct 22, 2011 #6
    so may i ask for b) and c)

    the ans is..h/2 or h(4R-4) / 3(3R-h)

    cuz my ans is not same as yours...

    btw where the ans for b and c are not the same
     
  8. Oct 22, 2011 #7

    vela

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    The answers you get for b and c should both be h/2.
     
  9. Oct 22, 2011 #8
    what do you get?
     
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