Question

Statement (A): Two artificial satellites revolving in the same circular orbit have the same period of revolution.
Statement (B): The orbital velocity is inversely proportional to the square root of the radius of the orbit.
Statement (C): The escape velocity of a body is independent of the altitude of the point of projection.

• A. A, B, C are true
• B. A, B true; C false
• C. A, C true; B false
• D. B, C true; A false

Hint:

Remember: \( T \propto r^{3/2} \), \( v_{orbital} \propto 1/\sqrt{r} \), and escape velocity varies with altitude.

Answer 1

The Correct Option is B

Statement A is true: Satellites in the same orbit have the same radius and hence same time period, derived from \( T = 2\pi \sqrt{\frac{r^3}{GM}} \).
Statement B is true: Orbital velocity is \( v = \sqrt{\frac{GM}{r}} \), which implies \( v \propto \frac{1}{\sqrt{r}} \).
Statement C is false: Escape velocity depends on the distance from the center of the Earth, i.e., altitude affects the value. \( v_{esc} = \sqrt{2gR} \) is valid only at surface.