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AP® Physics C: Mechanics

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Gravitational Force: Two Different Spheres Touching

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There are two spheres with constant, identical density wearing army clothes (they're uniform spheres in uniform!). The first has a mass of $M$ and a radius of $r$, and the second has a mass of $8M$ and a radius of $2r$.

What is the gravitational force between them if they are touching?

A

$\cfrac { 4G{ M }^{ 2 } }{9 { r }^{ 2 } } $

B

$\cfrac { 8G{ M }^{ 2 } }{9 { r }^{ 2 } } $

C

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

D

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

E

$\cfrac {72 G{ M }^{ 2 } }{ { r }^{ 2 } } $