anonymous
  • anonymous
INTEGRATION The inner and outer radii of a half hollow sphere are a and b.Find the center of gravity.Please help
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Through intergration
anonymous
  • anonymous
You have to consider this as a solid sphere and then integrate from a to b right?
anonymous
  • anonymous
You have to consider this as a solid sphere and then integrate from a to b right?

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More answers

geerky42
  • geerky42
Can you help? @ganeshie8 @zepdrix
anonymous
  • anonymous
I know the answer but don't know how to prove
Elsa213
  • Elsa213
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
anonymous
  • anonymous
Nope
zepdrix
  • zepdrix
center of gravity? .... wh... ut? 0_o
geerky42
  • geerky42
Nothing to do with moment of inertia lol
geerky42
  • geerky42
I think it's best that you define for us exactly what "center of gravity" is. @Zupari
geerky42
  • geerky42
Looks more like question for physicist, not mathematician lol.
anonymous
  • anonymous
Sorry i don't know the exact english word but i think thats the word
anonymous
  • anonymous
Centre of gravity of a hollow sphere is a/2 likewise you have to integrate and find the point of this object
zepdrix
  • zepdrix
the translation is fine :) im just not familiar with the concept. hmm
ganeshie8
  • ganeshie8
is it a complete sphere or an hemisphere ?
anonymous
  • anonymous
hemishpere
ganeshie8
  • ganeshie8
because if it were a complete sphere, dont u think the center of gravity just lies at the center
ganeshie8
  • ganeshie8
ohk..
geerky42
  • geerky42
Complete sphere would be more trivial, but he still have to prove it either way.
anonymous
  • anonymous
answer is 3{(a+b)(a^2 + b^2)}/8( a^2 + ab + b^2)
ganeshie8
  • ganeshie8
do you mean (0, 0, 3{(a+b)(a^2 + b^2)}/8( a^2 + ab + b^2))
anonymous
  • anonymous
i think so
anonymous
  • anonymous
https://www.youtube.com/watch?v=UiAH-Ev6PRA watch this if u don't know the concept.
anonymous
  • anonymous
likewise you have to apply that to this boy.
anonymous
  • anonymous
dont know how but i
anonymous
  • anonymous
yoda
dan815
  • dan815
|dw:1436562405371:dw|
anonymous
  • anonymous
yep
dan815
  • dan815
|dw:1436562485331:dw|
anonymous
  • anonymous
|dw:1436562465745:dw|
dan815
  • dan815
oh thats beautiful
dan815
  • dan815
i like this simplification, just find it for 2 circles
dan815
  • dan815
|dw:1436562542334:dw|
anonymous
  • anonymous
i cant get the given answer
dan815
  • dan815
by symmetry the center x is the origin now just determine y center
anonymous
  • anonymous
its not that simple you have to integrate
dan815
  • dan815
|dw:1436562726374:dw|
dan815
  • dan815
can you think of how to write that with integration
dan815
  • dan815
or u can try to find the mean radius too that is fine
dan815
  • dan815
i am thinking of this one geometrical way, maybe it works maybe it doesnt take al ook at it
dan815
  • dan815
how about finding a point such that the sum of all the vectors from the edge will equal 0
dan815
  • dan815
|dw:1436562918280:dw|
anonymous
  • anonymous
\[\int\limits_{a}^bb ^{2}x - x ^{3}/\int\limits_{a}^b a ^{2} - x ^{2}\]
anonymous
  • anonymous
by solving this i dont get the given answer
dan815
  • dan815
find this out though because there might be a really nice way if u get this
dan815
  • 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
anonymous
  • 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
dan815
  • dan815
im in canada
anonymous
  • anonymous
im in sri lanka if u've heard
dan815
  • dan815
yes ofcourse
anonymous
  • anonymous
cool
dan815
  • dan815
okay wait, so how did u get those 2 integrals
dan815
  • dan815
\[ \int\limits_{a}^bb ^{2}x - x ^{3}/\int\limits_{a}^b a ^{2} - x ^{2} \]
anonymous
  • anonymous
|dw:1436563494387:dw|
anonymous
  • anonymous
m for mass
anonymous
  • anonymous
p for density
dan815
  • dan815
okay
dan815
  • dan815
well we can ignore that since we are assume its homogenous, we are finding center of volume, but continue
anonymous
  • anonymous
|dw:1436563681149:dw|
dan815
  • dan815
ok yes
anonymous
  • anonymous
since the solid part is from a to b integral is from a to b BUT I CANT GET THE ANSWER
dan815
  • dan815
okay try this
dan815
  • dan815
|dw:1436563948647:dw|
dan815
  • dan815
|dw:1436564233941:dw|
dan815
  • dan815
|dw:1436564253565:dw|
dan815
  • dan815
does this make sense? we are finding the mean height
anonymous
  • anonymous
uhhh...i dont know how to solve that square root inside integral our syllabus doesn;t include that part
anonymous
  • anonymous
oh wait
dan815
  • dan815
ya u have to convert to polar coord
dan815
  • dan815
here is a better way from polar
dan815
  • dan815
|dw:1436564634557:dw|
anonymous
  • anonymous
just forget it
dan815
  • dan815
wait why dont give up
dan815
  • dan815
|dw:1436565276032:dw|
dan815
  • dan815
|dw:1436565312287:dw|
dan815
  • dan815
solve that integral
dan815
  • dan815
|dw:1436565419033:dw|
dan815
  • dan815
|dw:1436565521848:dw|

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