Question

Consider two satellites, $S_1$ and $S_2$ with periods of revolution, $1\text{hr}$ and $8\text{hr}$ 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. $1:2$
• B. $1:8$
• C. $8:1$
• D. $2:1$

Answer 1

The correct option is C $8:1$

Given:
Ratio of time periods,
$\frac{T_1}{T_2}=\frac{1}{8}$

We know that,
$\omega =\frac{2\pi }{T}$

$\Rightarrow \omega \propto \frac{1}{T}$

$\Rightarrow \frac{{\omega }_1}{{\omega }_2}=\frac{T_2}{T_1}$

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

$\Rightarrow {\omega }_1:{\omega }_2=8:1$