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Two identical spheres are touching. Both spheres are enlarged simultaneously, while their densities remain constant. The initial gravitational force between them is ${F}_{0}$and their initial radii are ${r}_{0}$.

Which relationship, as a function of $r$, represents the magnitude of the gravitational force as the radius of the spheres is increased?

A

${ F }_{ g }(r)={ F }_{ 0 }{ \left( \cfrac { { r }_{ 0 }}{ r } \right) }^{ 2 }$

B

${ F }_{ 0 }$

C

${ F }_{ g }(r)={ F }_{ 0 }{ \left( \cfrac { r }{ { r }_{ 0 } } \right) }^{ 2 }$

D

${ F }_{ g }(r)={ F }_{ 0 }{ \left( \cfrac { r }{ { r }_{ 0 } } \right) }^{ 4 }$

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