A satellite A of mass m is at a distance o

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A satellite $A$ of mass $m$ is at a distance of $r$ from the centre of the earth. Another satellite $B$ of mass $2m$ is at a distance of $2r$ from the earth's centre. Their time periods are in the ratio of

A

$1:2$

B

$1:16$

C

$1:32$

D

$1:2\sqrt 2 $

A satellite $A$ of mass $m$ is at a distance of $r$ from the centre of the earth. Another satellite $B$ of mass $2m$ is at a distance of $2r$ from the earth's centre. Their time periods are in the ratio of

Mass of the satellite does not effects on time period
$\frac{{{T_A}}}{{{T_B}}} = {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^{3/2}} = {\left( {\frac{r}{{2r}}} \right)^{3/2}} = {\left( {\frac{1}{8}} \right)^{1/2}} = \frac{1}{{2\sqrt 2 }}$