If the distance between two masses is tripled, how does the gravitational force

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Question: If the distance between two masses is tripled, how does the gravitational force change?

Options:

Correct Answer: It becomes 1/9

Solution:

F ∝ 1/r²; if r is tripled, F becomes F/9.

If the distance between two masses is tripled, how does the gravitational force change?

If the distance between two masses is tripled, how does the gravitational force change?

Step 1: Understand that gravitational force (F) between two masses depends on the distance (r) between them.
Step 2: Remember the formula for gravitational force: F ∝ 1/r². This means that the force is inversely proportional to the square of the distance.
Step 3: If the distance (r) is tripled, we can express this as r becomes 3r (where r is the original distance).
Step 4: Substitute 3r into the formula: F ∝ 1/(3r)².
Step 5: Calculate (3r)², which equals 9r².
Step 6: Now the formula looks like this: F ∝ 1/(9r²).
Step 7: This means that the new gravitational force (F') is F/9, where F is the original force.
Step 8: Conclude that if the distance between the two masses is tripled, the gravitational force becomes one-ninth of the original force.

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