Topic: Engineering Mechanics
Two satellites, of masses m and 2m, are on the same circular orbit around earth. If the velocity of the lighter satellite is $v_{0}$, what is the velocity of the heavier satellite?
- A. $\frac{1}{2}v_{0}$
- B. $v_{0}$
- C. $2v_{0}$
- D. $\frac{1}{4}v_{0}$
Answer: B. $v_{0}$
Explanation: Centrifugal force and Gravitational force both are acting on satellites while orbiting. For equilibrium, $m\frac{V_{0}^{2}}{r} = \frac{G \cdot M \cdot m}{r^{2}} \implies V_{0} = \sqrt{\frac{GM}{r}}$. Radius of orbit is same for both satellites and there is no effect of change of mass of the satellite on speed. So speed will be same for both satellites ($v_{0}$).