If the distance between two masses doubles, what happens to the gravitational force?

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Multiple Choice

If the distance between two masses doubles, what happens to the gravitational force?

Explanation:
Gravitational force follows an inverse-square relationship: the force between two masses is proportional to 1 over the distance between them squared. If the separation doubles, the denominator becomes 4, so the force becomes one quarter of its original value. In equation form, F = G m1 m2 / r^2; replacing r with 2r gives F' = G m1 m2 / (2r)^2 = (1/4) G m1 m2 / r^2 = F/4. The magnitude decreases to a quarter, while the direction stays along the line connecting the two masses.

Gravitational force follows an inverse-square relationship: the force between two masses is proportional to 1 over the distance between them squared. If the separation doubles, the denominator becomes 4, so the force becomes one quarter of its original value. In equation form, F = G m1 m2 / r^2; replacing r with 2r gives F' = G m1 m2 / (2r)^2 = (1/4) G m1 m2 / r^2 = F/4. The magnitude decreases to a quarter, while the direction stays along the line connecting the two masses.

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