Question

The ratio of angular velocity of two satellites at a distance $ r $ and $ 2r $ from the centre of the earth is:

• A. \( 1:1 \)
• B. \( 1:2 \)
• C. \( 2:1 \)
• D. \( 4:1 \)

Hint:

The angular velocity of a satellite is inversely proportional to the 3/2 power of the radius of its orbit.

Answer 1

The Correct Option is C

The angular velocity \( \omega \) of a satellite is given by: \[ \omega = \sqrt{\frac{GM}{r^3}} \] Where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( r \) is the radius of the orbit. For two satellites at distances \( r \) and \( 2r \), the ratio of angular velocities is: \[ \frac{\omega_1}{\omega_2} = \frac{\sqrt{\frac{GM}{r^3}}}{\sqrt{\frac{GM}{(2r)^3}}} = \frac{\sqrt{1}}{\sqrt{\frac{1}{8}}} = 2 \]
Thus, the ratio of angular velocities is \( 2:1 \).