Question:
Statement (A): Two artificial satellites revolving in the same circular orbit have same period of revolution.
Statement (B): The orbital velocity is inversely proportional to the square root of radius of the orbit.
Statement (C): The escape velocity of the body is independent of the altitude of the point of projection.
Statement (A): Two artificial satellites revolving in the same circular orbit have same period of revolution.
Statement (B): The orbital velocity is inversely proportional to the square root of radius of the orbit.
Statement (C): The escape velocity of the body is independent of the altitude of the point of projection.
Statement (B): The orbital velocity is inversely proportional to the square root of radius of the orbit.
Statement (C): The escape velocity of the body is independent of the altitude of the point of projection.
Show Hint
Remember:
\[
v_{\text{orbital}}=\sqrt{\frac{GM}{r}}
\]
and
\[
v_{\text{escape}}=\sqrt{\frac{2GM}{r}}
\]
Both depend on the orbital radius \(r\).
Updated On: Jun 22, 2026
- A, B, C are true
- A, B true and C false
- A, C true and B false
- B, C true and A false
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Check Statement (A).
The time period of a satellite revolving in a circular orbit is \[ T=2\pi\sqrt{\frac{r^3}{GM}} \] where \[ r=\text{radius of orbit} \] For satellites moving in the same circular orbit, the value of \(r\) is the same.
Hence, both satellites have the same period of revolution.
Therefore, Statement (A) is true.
Step 2: Check Statement (B).
Orbital velocity of a satellite is given by \[ v=\sqrt{\frac{GM}{r}} \] Thus, \[ v\propto \frac{1}{\sqrt{r}} \] Hence, orbital velocity is inversely proportional to the square root of the orbital radius.
Therefore, Statement (B) is true.
Step 3: Check Statement (C).
Escape velocity is given by \[ v_e=\sqrt{\frac{2GM}{R+h}} \] where \[ h=\text{altitude above Earth's surface} \] Clearly, escape velocity depends on altitude. As altitude increases, escape velocity decreases.
Hence, Statement (C) is false.
Step 4: Final conclusion.
Therefore, \[ \boxed{\text{A and B are true, while C is false}} \]
The time period of a satellite revolving in a circular orbit is \[ T=2\pi\sqrt{\frac{r^3}{GM}} \] where \[ r=\text{radius of orbit} \] For satellites moving in the same circular orbit, the value of \(r\) is the same.
Hence, both satellites have the same period of revolution.
Therefore, Statement (A) is true.
Step 2: Check Statement (B).
Orbital velocity of a satellite is given by \[ v=\sqrt{\frac{GM}{r}} \] Thus, \[ v\propto \frac{1}{\sqrt{r}} \] Hence, orbital velocity is inversely proportional to the square root of the orbital radius.
Therefore, Statement (B) is true.
Step 3: Check Statement (C).
Escape velocity is given by \[ v_e=\sqrt{\frac{2GM}{R+h}} \] where \[ h=\text{altitude above Earth's surface} \] Clearly, escape velocity depends on altitude. As altitude increases, escape velocity decreases.
Hence, Statement (C) is false.
Step 4: Final conclusion.
Therefore, \[ \boxed{\text{A and B are true, while C is false}} \]
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