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23 Jan 2020, 02:14
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D
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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%
Are You Up For the Challenge: 700 Level Questions
A. 50%
B. 200%
C. 300%
D. 500%
E. 600%
Are You Up For the Challenge: 700 Level Questions
23 Jan 2020, 05:12
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Bunuel
Let the masses of Asteroids A, B & C be \(m_A\), \(m_B\) & \(m_C\) respectively
& the distance between Asteroids A & B = \(d_1\) & distance between Asteroids A & C = \(d_2\)
--> Given, \(d_1 = 2*d_2\)
The gravitational force between Asteroid A and Asteroid B is equal to 9
--> \(9 = G\frac{m_A*m_B}{(d_1)^2}\) ....... (1)
The gravitational force between Asteroid A and Asteroid C is 6
--> \(6 = G\frac{m_A*m_C}{(d_2)^2}\) ....... (2)
(1) ÷ (2),
--> \(\frac{9}{6} = G\frac{m_A*m_B}{(d_1)^2}/G\frac{m_A*m_C}{(d_2)^2}\)
--> \(\frac{3}{2} = \frac{m_B}{m_C}*(\frac{d_2}{d_1})^2 = \frac{m_B}{m_C}*(\frac{1}{2})^2\)
--> \(\frac{m_B}{m_C} = \frac{3}{2}*4 = 6\)
--> \(m_B = 6*m_C\)
% greater = \(\frac{(m_B - m_C)}{m_C}*100 = \frac{6*m_C - m_C}{m_C}*100 = 500\)
Option D
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23 Jan 2020, 10:35
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\(A\) = Mass of Asteroid A
\(B\) = Mass of Asteroid B
\(C\) = Mass of Asteroid C
\(x\) = Distance between Asteroid A and Asteroid C
\(\frac{G*A*C}{x^2} = 6 \)
\(\frac{G*A}{x^2} = \frac{6}{C}\)
Also, \(\frac{G*A*B}{(2x)^2}=\frac{G*A*B}{4x^2}=9\)
We can rewrite this as, \([\frac{G*A}{x^2}]*[\frac{B}{4}]=9\) or \([\frac{6}{C}]*[\frac{B}{4}]=9\)
So \(B=6C\)
Percentage difference = \(\frac{B-C}{C}=\frac{6C-C}{C}=5\) or \(500\)%
Answer is (D)
\(B\) = Mass of Asteroid B
\(C\) = Mass of Asteroid C
\(x\) = Distance between Asteroid A and Asteroid C
\(\frac{G*A*C}{x^2} = 6 \)
\(\frac{G*A}{x^2} = \frac{6}{C}\)
Also, \(\frac{G*A*B}{(2x)^2}=\frac{G*A*B}{4x^2}=9\)
We can rewrite this as, \([\frac{G*A}{x^2}]*[\frac{B}{4}]=9\) or \([\frac{6}{C}]*[\frac{B}{4}]=9\)
So \(B=6C\)
Percentage difference = \(\frac{B-C}{C}=\frac{6C-C}{C}=5\) or \(500\)%
Answer is (D)
