The minimum time period of revolution of an artifical satellite is eq…

The time period of revolution T = $2 \pi / \omega$ where $\omega$ can be given as

$mr \omega^2 =\frac{GMm}{r^2}$

$\Rightarrow \omega =\sqrt{\frac{GM}{r^3}}$

$\Rightarrow T=\frac{2 \pi}{\omega} \omega=2 \pi \sqrt{\frac{r^3}{GM}}$

T is minimum when r is minimum. $\gamma_{\min}$ = R

$\Rightarrow T_{\min }=2 \pi \sqrt{\frac{r^3}{GM}}=2 \pi \sqrt{\frac{R}{g}}$

$=2 \pi \sqrt{\frac{6400 \times 10^3}{9.8}}$ sec = 82 min