Practicing Success
The minimum time period of revolution of an artifical satellite is equal to (M = mass of earth, R = radius of earth, g = 9.8 m/s2 |
$2 \pi \sqrt{R^2 / G M}$ 82 min $2 \pi \sqrt{R / g}$ All of the above |
All of the above |
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 |