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Through intergration

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

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

Can you help? @ganeshie8 @zepdrix

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

Nope

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

Nothing to do with moment of inertia lol

Looks more like question for physicist, not mathematician lol.

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

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

is it a complete sphere or an hemisphere ?

hemishpere

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

ohk..

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

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

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

i think so

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

likewise you have to apply that to this boy.

dont know how but i

yoda

|dw:1436562405371:dw|

yep

|dw:1436562485331:dw|

|dw:1436562465745:dw|

oh thats beautiful

i like this simplification, just find it for 2 circles

|dw:1436562542334:dw|

i cant get the given answer

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

its not that simple you have to integrate

|dw:1436562726374:dw|

can you think of how to write that with integration

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

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

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

|dw:1436562918280:dw|

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

by solving this i dont get the given answer

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

im in canada

im in sri lanka if u've heard

yes ofcourse

cool

okay wait, so how did u get those 2 integrals

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

|dw:1436563494387:dw|

m for mass

p for density

okay

|dw:1436563681149:dw|

ok yes

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

okay try this

|dw:1436563948647:dw|

|dw:1436564233941:dw|

|dw:1436564253565:dw|

does this make sense? we are finding the mean height

oh wait

ya u have to convert to polar coord

here is a better way from polar

|dw:1436564634557:dw|

just forget it

wait why dont give up

|dw:1436565276032:dw|

|dw:1436565312287:dw|

solve that integral

|dw:1436565419033:dw|

|dw:1436565521848:dw|