Satellites - Orbital Velocity & Period question from MHT CET 2026 (13 May, Shift 1)

Answer: (d)

1. For a geostationary satellite, gravity gives the centripetal force: $\frac{GMm}{r^2} = m\omega^2 r$, where $\omega$ is the earth's angular velocity.
2. So $r^3 = \frac{GM}{\omega^2}$, and $GM = gR^2$.
3. $r^3 = \frac{R^2 g}{\omega^2}$
4. So the answer is (d) $\frac{R^2g}{\omega^2}$.