Periodic time of a satellite revolving abo

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Periodic time of a satellite revolving above Earth’s surface at a height equal to $R$, radius of Earth, is $R$ [$g$ is acceleration due to gravity at Earth’s surface]

A

$2\pi \sqrt {\frac{{2R}}{g}} $

B

$4\sqrt 2 \pi \sqrt {\frac{R}{g}} $

C

$2\pi \sqrt {\frac{R}{g}} $

D

$8\pi \sqrt {\frac{R}{g}} $

Periodic time of a satellite revolving above Earth’s surface at a height equal to $R$, radius of Earth, is $R$ [$g$ is acceleration due to gravity at Earth’s surface]

$T = 2\pi \sqrt {\frac{{{{(R + h)}^3}}}{{g{R^2}}}}  $

$= 2\pi \sqrt {\frac{{{{(2R)}^3}}}{{g{R^2}}}}$

$ = 4\sqrt {2\pi } \sqrt {\frac{R}{g}} $