If $g \propto \frac{1}{R^{3}}$ (instead of $\frac{1}{R^{2}}),$ then the relation between time period of a satellite near earth's surface and radius R will be

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$T^{2} \propto R$

$T \propto R$

$T^{2} \propto R^{3}$

$T \propto R^{2}$

answer is B.

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Detailed Solution

Gravitational force provides the required centripetal force $m ω^{2} R = \frac{G M m}{R^{3}} \Rightarrow \frac{4 π^{2}}{T^{2}} = \frac{G M}{R^{4}} \Rightarrow T^{2} \propto R^{4} \Rightarrow T \propto R^{2}$

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