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7.Gravitation
normal
A satellite can be in a geostationary orbit around a planet at a distance $r$ from the centre of the planet. If the angular velocity of the planet about its axis doubles, a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is
A
$\frac{r}{2}$
B
$\frac{r}{{2\sqrt 2 }}$
C
$\frac{r}{{{{\left( 4 \right)}^{1/3}}}}$
D
$\frac{r}{{{{\left( 2 \right)}^{1/3}}}}$
Solution
Angular speed of earth $=$ angular speed of geostationary satellite
If $\omega$ is doubled, time period becomes half using $T=\frac{2 \pi}{\omega}$
Thus we get
$T^{2} \propto r^{3}$
or
$r^{\prime}=\frac{r}{4^{1 / 3}}$
Standard 11
Physics
