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

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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.

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