Question

Consider two satellites $S_1$ and $S_2$ with periods of revolution 1 hr. and 8 hr. 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

Hint:

Angular velocity is inversely proportional to the time period. You don't need Kepler's 3rd law ($T^2 \propto R^3$) unless the question asks for orbital radii.

Answer 1

The Correct Option is A

Step 1: Angular velocity $\omega$ is related to time period $T$ by $\omega = \frac{2\pi}{T}$.
Step 2: Therefore, $\frac{\omega_1}{\omega_2} = \frac{T_2}{T_1}$.
Step 3: Given $T_1 = 1$ hr and $T_2 = 8$ hr.
Step 4: $\frac{\omega_1}{\omega_2} = \frac{8}{1}$.