Which of the following quantities is inversely proportional to the gravitational pull between two objects?
A. The sum of their masses
B. The sum of their volumes
C. The square of the distance that separates them
D. The distance from their center to their surface
Answer (2)
The gravitational force between two objects is described by Newton's law: F = G " , ( m 1 m 2 ) / ( r 2 ) .
Analyze the relationship between the gravitational force and the given options.
Identify that the gravitational force is inversely proportional to the square of the distance between the objects.
Conclude that the correct answer is the square of the distance that separates them: The square of the distance that separates them
Explanation
Problem Analysis We need to identify which quantity is inversely proportional to the gravitational pull between two objects, based on Newton's law of universal gravitation.
Recalling Newton's Law Newton's law of universal gravitation states that the gravitational force (F) between two objects is given by the formula: F = G " , ( m 1 m 2 ) / ( r 2 ) where:
G is the gravitational constant,
m 1 and m 2 are the masses of the two objects,
r is the distance between the centers of the two objects.
Analyzing the Options Now, let's analyze each option:
The sum of their masses: The formula shows that F is proportional to the product of the masses ( m 1 m 2 ), not the sum ( m 1 + m 2 ). Therefore, this option is incorrect.
The sum of their volumes: The formula does not include volume, so this option is incorrect.
The square of the distance that separates them: The formula shows that F is inversely proportional to the square of the distance ( r 2 ). This means as r 2 increases, F decreases, and vice versa. Therefore, this option is correct.
The distance from their center to their surface: This is related to the size of the objects but not directly related to the gravitational force in the formula. Therefore, this option is incorrect.
Conclusion Based on the analysis, the quantity that is inversely proportional to the gravitational pull between two objects is the square of the distance that separates them.
Examples
Understanding inverse proportionality is crucial in many real-world scenarios. For instance, the intensity of light from a lamp decreases as you move farther away. Similarly, the gravitational force weakens as the distance between objects increases. This concept helps in designing satellite orbits, understanding planetary motion, and even optimizing wireless communication signals.
The quantity that is inversely proportional to the gravitational pull between two objects is the square of the distance that separates them, according to Newton's law of universal gravitation. Therefore, the correct choice is C. The square of the distance that separates them.
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