Question

Consider two satellites $S_1$ and $S_2$ with periods of revolution $1hr$ and $8hr$ respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite $S_1$ to the angular velocity of satellite $S_2$ is

• A. $8:1$
• B. $1:8$
• C. $2:1$
• D. $1:4$

Answer 1

The correct option is A

$8:1$

Step 1. Given data

The time period of the satellite, $S_1,T_1=1hr$

The time period of the satellite, $S_2,T_2=8hr$

Step 2. Finding the ratio of the Angular velocity of both the satellites

By using the formula of the angular velocity,$\omega$

$\omega =\frac{2\mathrm{\pi }}{T}$

Angular velocity of the first satellite, ${\omega }_1=\frac{2\mathrm{\pi }}{1}$

${\omega }_1=2\mathrm{\pi }$

Angular velocity of the second satellite, ${\omega }_2=\frac{2\mathrm{\pi }}{8}$

$\frac{{\omega }_1}{{\omega }_2}=\frac{8}{1}$

Therefore,${\omega }_1:{\omega }_2=8:1$

Hence, the correct option is $\left(A\right)$.