\[(a)\;R^3 \quad (b)\;R^{\frac{7}{2}} \quad (c)\;R^{\frac{3}{2}} \quad (d)\;R^{\frac{9}{2}}\]

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Gravitational force $ \alpha\;R ^{\large\frac{-5}{2}}$

Centripelal force $\alpha\; R^{\large\frac{-5}{2}}$

$m R w^2 \;\alpha\; R^{\large\frac{-5}{2}}$

$w^2 \;\alpha \; R^{\large\frac{-5}{2} -1}$

$w^2 \;\alpha \; R^{\large\frac{-7}{2}}$

$\large\bigg(\frac{2 \pi}{T}\bigg)^2 \alpha\; $$R^{\large\frac{-7}{2}}$

$T^2 \alpha\; R^{\large\frac{7}{2}}$

Hence b is the correct answer.

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