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

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

Options:

Correct Answer: It becomes four times weaker

Solution:

According to the inverse square law, if the distance is doubled, the force becomes 1/(2^2) = 1/4 of the original force.

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

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

Correct Answer: 1/4 of the original force

Step 1: Understand that gravitational force depends on the distance between two masses.
Step 2: Know that the formula for gravitational force is F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them.
Step 3: If the distance (r) is doubled, it becomes 2r.
Step 4: Substitute 2r into the formula: F' = G * (m1 * m2) / (2r)^2.
Step 5: Simplify (2r)^2 to get 4r^2, so the new force is F' = G * (m1 * m2) / 4r^2.
Step 6: Compare the new force F' to the original force F: F' = 1/4 * F.
Step 7: Conclude that if the distance is doubled, the gravitational force becomes 1/4 of the original force.

Gravitational Force – The gravitational force between two masses is described by Newton's law of universal gravitation, which states that the force is inversely proportional to the square of the distance between the centers of the two masses.
Inverse Square Law – This law indicates that if the distance between two objects is increased, the gravitational force decreases by the square of the distance increase.