Question

The radii of circular orbits of two satellites \( A \) and \( B \) of the earth are \( R \) and \( R' \) respectively, where \( R \) is the radius of the earth. If the speed of satellite \( B \) is 6 V, then the speed of satellite \( A \) will be

• A. 3 V
• B. 4 V
• C. 12 V
• D. \( \frac{3}{2} \) V

Hint:

The orbital speed of a satellite depends on the square root of the inverse of the radius of the orbit. Smaller orbits correspond to higher speeds.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The orbital speed of a satellite depends on the radius of its orbit. We need to find the speed of satellite \( A \) given its radius and the orbital parameters of satellite \( B \).
Step 2: Key Formula or Approach:
Orbital speed \( v = \sqrt{\frac{GM}{r}} \).
This implies \( v \propto \frac{1}{\sqrt{r}} \).
Step 3: Detailed Explanation:
For satellite \( A \), radius \( r_A = 4R \).
For satellite \( B \), radius \( r_B = R \).
Taking the ratio of their orbital speeds:
\[ \frac{v_A}{v_B} = \sqrt{\frac{r_B}{r_A}} = \sqrt{\frac{R}{4R}} = \sqrt{\frac{1}{4}} = \frac{1}{2} \]
Given \( v_B = 6\text{ V} \):
\[ v_A = \frac{v_B}{2} = \frac{6\text{ V}}{2} = 3\text{ V} \]
Step 4: Final Answer:
The speed of satellite \( A \) is \( 3\text{ V} \).