A satellite can be in a geostationary orbit around earth at a distance $$r$$ from the centre. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth if its distance from the centre is
A.
$$\frac{r}{2}$$
B.
$$\frac{r}{{2\sqrt 2 }}$$
C.
$$\frac{r}{{{{\left( 4 \right)}^{\frac{1}{3}}}}}$$
D.
$$\frac{r}{{{{\left( 2 \right)}^{\frac{1}{3}}}}}$$
Solution :
Angular speed of earth = angular speed of geostationary satellite.
If $$\omega $$ is double, time period become half using $${T^2} \propto {{r'}^3}$$
$$r' = \frac{r}{{{4^{\frac{1}{3}}}}}$$
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