A geostationary satellite

Question:

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

  1. $6 \sqrt{2}$

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

  3. 3

  4. 5


Correct Option: , 3

Solution:

(3) $\mathrm{T} \propto \mathrm{R}^{3 / 2}$

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

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