Two satellites `S_1` and `S_2` revolve around the earth at distances `3R` and `6R` from the centre of the earth. Find the ratio of their (a) linear speeds and (b) angular speeds.

Explanation

To solve the problem of finding the ratio of linear speeds and angular speeds of two satellites \( S_1 \) and \( S_2 \) revolving around the Earth at distances \( 3R \) and \( 6R \) from the center of the Earth, we can follow these steps:

### Step 1: Understand the gravitational force and centripetal force
The gravitational force acting on a satellite is given by:
\[ F_g = \frac{GMm}{r^2} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, \( m \) is the mass of the satellite, and \( r \) is the distance from the center of the Earth.
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