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Question
What happens to the force between two objects, if the distance between the objects is doubled and tripled?
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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