If the distance between two objects is doubled, how does the gravitational force

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Question: If the distance between two objects is doubled, how does the gravitational force between them change?

Options:

Correct Answer: It becomes one-fourth

Solution:

Gravitational force F ∝ 1/r². If r is doubled, F becomes F/4.

If the distance between two objects is doubled, how does the gravitational force between them change?

If the distance between two objects is doubled, how does the gravitational force between them change?

Step 1: Understand that gravitational force depends on the distance between two objects.
Step 2: Know the formula for gravitational force: F ∝ 1/r², where F is the gravitational force and r is the distance between the objects.
Step 3: If the distance (r) is doubled, write it as 2r.
Step 4: Substitute 2r into the formula: F ∝ 1/(2r)².
Step 5: Calculate (2r)², which equals 4r².
Step 6: Now the formula looks like F ∝ 1/(4r²).
Step 7: This means the new gravitational force is F/4, indicating that the force is reduced to a quarter of its original value.

Inverse Square Law – The gravitational force between two objects is inversely proportional to the square of the distance between them.