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What is the gravitational force between two identical uniform spheres (each with a mass of $M$ and a radius of $r$) that are touching?

0, because they are touching.

$\frac { G{ M }^{ 2 } }{ { r }^{ 2 } } $

$\frac { G{ M }^{ 2 } }{2{ r }^{ 2 } } $

$\frac { G{ M }^{ 2 } }{ 4{ r }^{ 2 } } $