6. The mass and radius of a spherical planet with a uniform density are $M$ and $R$ respectively. The planet constantly rotates with a period $T$. The free-fall acceleration $g_{p}$ at the pole of the planet (where the rotation axis passes through) and the free-fall acceleration $g_{e}$ at the equator of the planet are related to each other by
(A)$g_{e} - g_{p} = \frac{4\pi^{2}R}{T^{2}}$
(B)$g_{e} - g_{p} = \frac{2\pi^{2}R}{T^{2}}$
(C)$g_{e} - g_{p} = -\frac{2\pi^{2}R}{T^{2}}$
(D)$g_{e} - g_{p} = -\frac{4\pi^{2}R}{T^{2}}$

(E)None of the above

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