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
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
${T^2} \propto {R^3}$
$T \propto {R^2}$
${T^2} \propto R$
$T \propto R$
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
Gravitational force provides the required centripetal force
$m{\omega ^2}R = \frac{{GMm}}{{{R^3}}}$
$ \Rightarrow $$\frac{{4{\pi ^2}}}{{{T^2}}} = \frac{{GM}}{{{R^4}}}$
$ \Rightarrow $$T \propto {R^2}$
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