How does the gravitational force between two objects change if the distance betw

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Question: How does the gravitational force between two objects change if the distance between them is halved?

Options:

Correct Answer: It quadruples

Solution:

According to Newton\'s law of gravitation, if the distance is halved, the force increases by a factor of 4 (F ∝ 1/r²).

How does the gravitational force between two objects change if the distance between them is halved?

How does the gravitational force between two objects change if the distance between them is halved?

Step 1: Understand that gravitational force depends on the distance between two objects.
Step 2: Remember Newton's law of gravitation, which states that the force (F) is inversely proportional to the square of the distance (r) between the objects: F ∝ 1/r².
Step 3: If the distance (r) is halved, we can express this as r/2.
Step 4: Substitute r/2 into the formula: F ∝ 1/(r/2)².
Step 5: Simplify the equation: F ∝ 1/(r²/4) = 4/r².
Step 6: This shows that the gravitational force increases by a factor of 4 when the distance is halved.

Newton's Law of Gravitation – The gravitational force between two objects is inversely proportional to the square of the distance between them (F ∝ 1/r²).