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# A satellite can be in a geostationary orbit around the earth at a distance r from the center. 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 center is

$(a)\;\frac{n}{2} \quad (b)\;\frac{r}{2 \sqrt 2} \quad (c)\;\frac{r}{(2)^{1/3}} \quad (d)\;\frac{n}{(4)^{1/3}}$

Angular speed of earth= angular speed of geostationary satellite
If w is doubled, time period becomes half.
Also $T^2 \; \alpha \;r^3$
$\bigg (\large\frac{T_1}{T_2}\bigg)^2= \bigg(\large\frac{r_1}{r_2}\bigg)^3$
$\bigg ( \large\frac{T_1}{T_1{/2}}\bigg)^2 =\frac{r_1^3}{r_2^3}$
$\bigg ( \large\frac{r_1}{r_2}\bigg)^3$$=4$
$r_2^3=\large \frac{r_1^3}{4}$
$r_2=\large\frac{r_1}{(4)^{1/3}}$
Hence d is the correct answer.
edited Jun 30, 2014