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Question
What happens to the force between two objects, if the distance between the objects is doubled and tripled?
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Solution
If the distance between the two objects is doubled, then
F'' = `(Gm_1m_2)/(2R^2)`
= `1/4 xx (Gm_1m_2)/(R^2)`
= `1/4` F
= `F/4`
Thus, the gravitational force between the two objects becomes one-fourth.
If the distance between the two objects is tripled, then
F′′′ = `(Gm_1m_2)/(3R)^2`
= `1/9 xx (Gm_1m_2)/R^2`
= `1/9 xx F`
= `F/9`
Thus, the gravitational force between the two objects becomes one-ninth.
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