Question

If the distance between two objects is increased by a factor of 7, how will the gravitational force between them will change?

Answer 1

Explanation:

If the distance between two objects is increased by a factor of 7, how will the gravitational force between them will change?

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Answer 2

Given info : the distance between two objects is increased by a factor of 7.

To find : how will the gravitational force between them will change ?

solution : let initial distance between the object was r.

now the distance between the objects is increased by a factor of 7.

so new distance between them will be 7r

we know from Newton's gravitational law,

gravitational force, F = GMm/r²

here it is clear that F is inversely proportional to r.

so if the distance between the object is increased, force will decrease.

mathematically,

F₁/F₂ = r₂²/r₁²

here, r₂ = 7r and r₁ = r

so, F₁/F₂ = 7r²/r² = 7²/1² = 49/1

⇒F₂ = F₁/49

Therefore the gravitational force between them will decrease and that is 1/49th of initial force between them.