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 given by F = G r 2 m 1 m 2 .
The force is inversely proportional to the square of the distance ( r 2 ) between the objects.
As the distance increases, the gravitational force decreases proportionally.
Therefore, the correct answer is the square of the distance that separates them: The square of the distance that separates them .
Explanation
Understanding the Problem The question asks us to identify which of the given options is inversely proportional to the gravitational pull between two objects. To solve this, we need to recall the formula for gravitational force and analyze how each option relates to it.
Recalling the Gravitational Force Formula The gravitational force ( F ) between two objects is described by the formula: F = G r 2 m 1 m 2 where: - G is the gravitational constant, - m 1 and m 2 are the masses of the two objects, and - r is the distance between the centers of the two objects.
Analyzing Each Option Now, let's examine each option in relation to the gravitational force: 1. The sum of their masses: The gravitational force is proportional to the product of the masses ( m 1 × m 2 ), not the sum. 2. The sum of their volumes: The formula for gravitational force doesn't involve the volumes of the objects. 3. The square of the distance that separates them: The gravitational force is inversely proportional to the square of the distance ( r 2 ). As r 2 increases, F decreases proportionally. 4. The distance from their center to their surface: This is not directly related to the gravitational force formula. The formula uses the distance between the centers of the objects.
Conclusion Based on the analysis, the gravitational force is inversely proportional to the square of the distance between the objects.
Examples
Understanding inverse proportionality is crucial in many real-world scenarios. For instance, the intensity of light from a lamp decreases with the square of the distance from the lamp. If you double the distance from the lamp, the light intensity becomes four times weaker. This principle applies not only to gravity but also to electromagnetism, sound, and other phenomena, helping us design lighting systems, understand signal propagation, and much more.
The gravitational pull between two objects is inversely proportional to the square of the distance that separates them, as indicated by the formula F = G r 2 m 1 m 2 . Therefore, the correct answer is option C: The square of the distance that separates them.
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