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The gravitational force between two objects,

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Tuck School Moderator
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The gravitational force between two objects,  [#permalink]

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New post 01 Sep 2018, 08:03
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  65% (hard)

Question Stats:

54% (02:24) correct 46% (02:51) wrong based on 55 sessions

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The gravitational force between two objects, F, is given by the formula \(F=G\frac{m×n}{r^2}\),where G is a constant, m and n are the masses of the two objects, and r is the distance between the two objects. The gravitational force between Asteroid A and Asteroid B is equal to 9, and the gravitational force between Asteroid A and Asteroid C is 6. If the distance between Asteroid A and Asteroid B is twice the distance between Asteroid A and Asteroid C, by what percent does the mass of Asteroid B exceed the mass of Asteroid C?
A. 50%
B. 200%
C. 300%
D. 500%
E. 600%

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Re: The gravitational force between two objects,  [#permalink]

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New post 01 Sep 2018, 08:40
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PeepalTree wrote:
The gravitational force between two objects, F, is given by the formula \(F=G\frac{m×n}{r^2}\),where G is a constant, m and n are the masses of the two objects, and r is the distance between the two objects. The gravitational force between Asteroid A and Asteroid B is equal to 9, and the gravitational force between Asteroid A and Asteroid C is 6. If the distance between Asteroid A and Asteroid B is twice the distance between Asteroid A and Asteroid C, by what percent does the mass of Asteroid B exceed the mass of Asteroid C?
A. 50%
B. 200%
C. 300%
D. 500%
E. 600%



Let the weights be A, B and C..
We are looking for \(\frac{B-C}{C}\)*100

Gravitational force between A and B= \(9=G\frac{A*B}{4d^2}\)...(I)

Gravitational force between A and C= \(6=G\frac{A*C}{d^2}\)...(II)

Divide I by II..
9/6=B/4C.....B/C=6.....(B/C)-1=6-1=5......(B-C)/C=5..
Therefore \(\frac{B-C}{C}\)*100= 5*100=500%

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Re: The gravitational force between two objects,   [#permalink] 01 Sep 2018, 08:40
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