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Assume that the Earth has a uniform density of $\rho$ and a radius of ${R}_{E}$.

What is the strength of the gravitational field at $r=\frac {{R}_{E}} {2}$, halfway to the center of the Earth in terms of ${R}_{E}$ and $\rho$?

A

$\cfrac { 4 }{ 3 } G\pi \rho { R }_{ E }^{ 3 }$

B

$\cfrac { 4 }{ 3 } G\pi \rho { R }_{ E }^{ 2 }$

C

$\cfrac { 4 }{ 3 } G\pi \rho { R }_{ E }$

D

$\cfrac { 2 }{ 3 } G\pi \rho { R }_{ E }$

E

$\cfrac { 2 }{ 3 } G\pi \rho { R }_{ E }^{ 3 }$

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