Question:
The time period of a satellite in a circular orbit of radius $\mathrm{R}$ is $\mathrm{T}$. The period
of another satellite in a circular orbit of radius $9 \mathrm{R}$ is:
Correct Option: , 2
Solution:
(2)
$\mathrm{T}^{2} \propto \mathrm{R}^{3}$
$\left(\frac{\mathrm{T}^{\prime}}{\mathrm{T}}\right)^{2}=\left(\frac{9 \mathrm{R}}{\mathrm{R}}\right)^{3}$
$\mathrm{~T}^{2}=\mathrm{T}^{2} \times 9^{3}$
$\mathrm{~T}=\mathrm{T} \times 3^{3}$
$\mathrm{~T}=27 \mathrm{~T}$