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The gravitational force between two objects, F, is given by the formul
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28 Jul 2021, 02:55
28 Jul 2021, 02:55
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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%
A. 50%
B. 200%
C. 300%
D. 500%
E. 600%
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Re: The gravitational force between two objects, F, is given by the formul
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28 Jul 2021, 21:32
28 Jul 2021, 21:32
GeminiHeat 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%
A. 50%
B. 200%
C. 300%
D. 500%
E. 600%
\(F_{AB} = 9\)
\(F_{AC} = 6\)
\(r_{AB} = 2r_{AC}\)
Let B and C be the masses of asteroids B and C resp.
\(\frac{F_{AB}}{F_{AC}} = (\frac{B}{r_{AB}^2})(\frac{r_{AC}^2}{C})\)
\(\frac{9}{6} = (\frac{B}{4r_{AC}^2})(\frac{r_{AC}^2}{C})\)
\(\frac{3}{2} = (\frac{B}{4})(\frac{1}{C})\)
\(6 = \frac{B}{C}\)
\(B = 6C\)
Percent change = \(\frac{B - C}{C} (100) = \frac{6C - C}{C} (100) = 500\)%
Hence, option D
gmatclubot
Re: The gravitational force between two objects, F, is given by the formul [#permalink]
28 Jul 2021, 21:32
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