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A certain plane completes one rotation about its axis in time \( T \). The weight of an object placed at the equator on the planet's surface is a fraction \( f(f \) is close to unity) of its weight recorded at a latitude of \( 60^{\circ} \). The density of the planet (assumed to be a uniform perfect sphere is given by)
[KVPY 2010]
(a) \( \frac{4-f}{1-f} \frac{3 \pi}{4 G T^{2}} \)
(b) \( \frac{4-f}{1+f} \frac{3 \pi}{4 G T^{2}} \)
(c) \( \frac{4-3 f}{1-f} \frac{3 \pi}{4 G T^{2}} \)
(d) \( \frac{4-2 f}{1-f} \frac{3 \pi}{4 G T^{2}} \)
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