Q157 / 170 · Manipal (MET) 2017 · Physics

A geo-stationary satellite is orbiting the earth at height of $6 R$ above the surface of the earth, $R$ being the radius of earth. The time period of another satellite at a height of $2.5 R$ from the surface of the earth is

  • A
    10 h
  • B
    $6 / \sqrt{2} h$
  • C
    6 h
  • Correct answer
    D
    $6 \sqrt{2} h$

Solution

Distance of the satellite from the centre are $7 R$ and 3.5 R respectively. $\begin{gathered} \frac{T_2}{T_1}=\left(\frac{R_2}{R_1}\right)^{3 / 2} \\ \Rightarrow T_2=24\left[\frac{3.5 R}{7 R}\right]^{3 / 2}=6 \sqrt{2} \mathrm{~h} \end{gathered}$

Hence, the correct answer is option: 'D'.

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