A geostationary satellite is orbiting around an arbitary planet ^{prime} P ^{prime} at a height

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7.Gravitation

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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

$\frac{6}{\sqrt{2}}$

C

$3$

D

$5$

(JEE MAIN-2021)

Solution

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

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

Standard 11

Physics

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