if two objects are moved closer together so that the distance between them is one-third the original distance what is the gravitational force after the object is moved

let the mass of the two objects be m₁ and m₂ respectively and the distance between the two objects be "r₁" initially.

the gravitational force between the two objects initially is then given as

F₁ = G m₁ m₂ / r₁² eq-1

where G = universal gravitational constant

when the objects are moved closer and the distance between the objects become one third of the original distance, hence

r₂ = distance after objects moved closer = r₁/3

new gravitational force between the objects after they are moved closed is given as

F₂ = G m₁ m₂ / r₂² eq-2

dividing eq-2 by eq-1

F₂/F₁ = (G m₁ m₂ / r₂²) / (G m₁ m₂ / r₁²)

F₂/F₁ = r₁²/r₂²

we know that, r₂ = r₁/3

hence

F₂/F₁ = r₁² / (r₁/3) ²

F₂/F₁ = 9

F₂ = 9 F₁

hence the gravitational force becomes nine times its initial value

Answer: D

Explanation:

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