The time period of a satellite in a circular orbit

Question:

The time period of a satellite in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius $9 \mathrm{R}$ is :

  1. $9 \mathrm{~T}$

  2. $27 \mathrm{~T}$

  3. $12 \mathrm{~T}$

  4. $3 \mathrm{~T}$


Correct Option: , 2

Solution:

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

$\left(\frac{T^{\prime}}{T}\right)^{2}=\left(\frac{9 R}{R}\right)^{3}$

$T^{\prime 2}=T^{2} \times 9^{3}$

$T^{\prime}=T \times 3^{3}$

$T^{\prime}=27 T$

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