A geostationary satellite is orbiting around an arbitary planet ^… - Vidyadip

MCQ

A geostationary satellite is orbiting around an arbitary planet $^{\prime} P ^{\prime}$ at a height of $11 R$ above the surface of $^{\prime} P ^{\prime} ,$ $R$ being the radius of $^{\prime} P .^{\prime}$ The time period of another satellite in hours at a height of $2R$ from the surface of $^{\prime} P ^{\prime}$ is $........$.$^{\prime} P ^{\prime}$ has the time period of $24\, hours.$

A
$6 \sqrt{2}$
B
$\frac{6}{\sqrt{2}}$
✓
$3$
D
$5$

✓

Answer

Correct option: C.

$3$

c
$T \propto R ^{3 / 2}$

$\frac{24}{ T }=\left(\frac{12 R }{3 R }\right)^{3 / 2} \Rightarrow T =3\, hr$

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