The time period of a satellite in a circular orbit of radius

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:

1. (1) $9 \mathrm{~T}$

2. (2) $27 \mathrm{~T}$

3. (3) $12 \mathrm{~T}$

4. (4) $3 \mathrm{~T}$

Correct Option: , 2

Solution:

(2)

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

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

$\mathrm{~T}^{2}=\mathrm{T}^{2} \times 9^{3}$

$\mathrm{~T}=\mathrm{T} \times 3^{3}$

$\mathrm{~T}=27 \mathrm{~T}$