- #1

timtng

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Please help me solve this problem.

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- Thread starter timtng
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- #1

timtng

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Please help me solve this problem.

- #2

HallsofIvy

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To start with basics, what do you understand the

- #3

PrudensOptimus

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F

R = sqrt((G*m

- #4

jamesrc

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I think by center of gravity he meant the RADIUS in Fg.

Actually, I think you want to approach this like a moment balance problem, where a force of 3Mg (the sum of the weights) is concentrated at the unknown x_cm (center of mass/gravity).

- #5

HallsofIvy

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jamesrc: I actually do know what "center of gravity" means! I asked timtng because I wanted to see what HIS understanding of the problem was.

timtng: In other words, shorn of all the unecessary "sphere" stuff, you have a line supporting two weights of mass M and 2M with distance 4R between them and want to find a "fulcrum point" where they will balance. Let x be the distance from mass M to the fulcrum. Mass M has weight Mg and so torque Mgx about the fulcrum. Mass 2M has weight 2Mg. It's distance from the fulcrum is 4R- x so its torque around the fulcrum is 2Mg(4R-x). In order to balance those must be equal: Mgx= 2Mg(4R-x). The first thing you can do is divide the equation by Mg to get x= 2(4R- x)= 8R- 2x. 3x= 8R so x= 8R/3.

- #6

jamesrc

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jamesrc: I actually do know what "center of gravity" means! I asked timtng because I wanted to see what HIS understanding of the problem was.

HallsofIvy: I had no doubt of

- #7

HallsofIvy

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Ah, I see your point. Thank you.

- #8

he may not be confused...what he means is really center of gravity...

center of gravity not necessarily taken just from one object..

in this case the

assume take point O at the center gravity of smaller sphere.

let w denotes the weight of smaller sphere.

so the Center gravity of the total body =2w*4r / 3w = (8/3)r from point O

it means the center of gravity lies on (5/3)r from lighter sphere or (1/3)r from weighter sphere and this center of gravity should lay in the line which connect the center gravity of lighter sphere and the center gravity from the weight one.

I wish this answer and explanation,will benefits you

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