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

- anonymous

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- anonymous

Through intergration

- anonymous

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

- 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

Can you help? @ganeshie8 @zepdrix

- anonymous

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

- 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

Nope

- zepdrix

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

- geerky42

Nothing to do with moment of inertia lol

- geerky42

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

- geerky42

Looks more like question for physicist, not mathematician lol.

- anonymous

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

- anonymous

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

- zepdrix

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

- ganeshie8

is it a complete sphere or an hemisphere ?

- anonymous

hemishpere

- ganeshie8

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

- ganeshie8

ohk..

- geerky42

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

- anonymous

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

- ganeshie8

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

- anonymous

i think so

- anonymous

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

- anonymous

likewise you have to apply that to this boy.

- anonymous

dont know how but i

- anonymous

yoda

- dan815

|dw:1436562405371:dw|

- anonymous

yep

- dan815

|dw:1436562485331:dw|

- anonymous

|dw:1436562465745:dw|

- dan815

oh thats beautiful

- dan815

i like this simplification, just find it for 2 circles

- dan815

|dw:1436562542334:dw|

- anonymous

i cant get the given answer

- dan815

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

- anonymous

its not that simple you have to integrate

- dan815

|dw:1436562726374:dw|

- dan815

can you think of how to write that with integration

- dan815

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

- dan815

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

- dan815

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

- dan815

|dw:1436562918280:dw|

- anonymous

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

- anonymous

by solving this i dont get the given answer

- dan815

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

- 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

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

im in canada

- anonymous

im in sri lanka if u've heard

- dan815

yes ofcourse

- anonymous

cool

- dan815

okay wait, so how did u get those 2 integrals

- dan815

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

- anonymous

|dw:1436563494387:dw|

- anonymous

m for mass

- anonymous

p for density

- dan815

okay

- dan815

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

- anonymous

|dw:1436563681149:dw|

- dan815

ok yes

- anonymous

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

- dan815

okay try this

- dan815

|dw:1436563948647:dw|

- dan815

|dw:1436564233941:dw|

- dan815

|dw:1436564253565:dw|

- dan815

does this make sense? we are finding the mean height

- anonymous

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

- anonymous

oh wait

- dan815

ya u have to convert to polar coord

- dan815

here is a better way from polar

- dan815

|dw:1436564634557:dw|

- anonymous

just forget it

- dan815

wait why dont give up

- dan815

|dw:1436565276032:dw|

- dan815

|dw:1436565312287:dw|

- dan815

solve that integral

- dan815

|dw:1436565419033:dw|

- dan815

|dw:1436565521848:dw|

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