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# The gravitational force between two objects,

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Tuck School Moderator
Status: Valar Dohaeris
Joined: 31 Aug 2016
Posts: 301
GMAT 1: 700 Q49 V37
The gravitational force between two objects,  [#permalink]

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01 Sep 2018, 08:03
4
00:00

Difficulty:

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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Joined: 02 Aug 2009
Posts: 8023
Re: The gravitational force between two objects,  [#permalink]

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01 Sep 2018, 08:40
1
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%

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