Two staellites A and B move round the earth in the same orbit . The mass of A is twice the mass of B .The quantity which is same for the two satellites will be

Options

A. Kinetic energy
B. Total energy
C. Potential energy
D. speed

Answer

To solve the problem, we need to analyze the motion of the two satellites A and B around the Earth. Given that they are in the same orbit, we can determine which quantities are the same for both satellites.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have two satellites, A and B, moving in the same orbit around the Earth.
- The mass of satellite A is twice that of satellite B (let's denote the mass of satellite B as m, then the mass of satellite A is 2m).

2. **Identifying Relevant Concepts**:
- For satellites in the same orbit, the gravitational force provides the necessary centripetal force for circular motion.
- The gravitational force acting on a satellite is given by \( F = \frac{G M m}{r^2} \), where \( M \) is the mass of the Earth, \( m \) is the mass of the satellite, \( r \) is the distance from the center of the Earth to the satellite, and \( G \) is the gravitational constant.

3. **Centripetal Force**:
- The centripetal force required for circular motion is given by \( F_c = \frac{m v^2}{r} \), where \( v \) is the orbital speed of the satellite.
- Setting the gravitational force equal to the centripetal force gives us:
\[ \frac{G M m}{r^2} = \frac{m v^2}{r} \]

4. **Solving for Orbital Speed**:
- We can cancel \( m \) from both sides (since it is non-zero) and rearranging gives:
\[ v^2 = \frac{G M}{r} \]
- Thus, the orbital speed \( v \) depends only on the mass of the Earth \( M \) and the radius \( r \) of the orbit, not on the mass of the satellite.

5. **Conclusion**:
- Since both satellites A and B are in the same orbit, they will have the same orbital speed \( v \).
- Other quantities like gravitational potential energy and kinetic energy will differ due to the different masses, but the orbital speed remains the same.

### Final Answer:
The quantity that is the same for both satellites A and B is the **orbital speed**.

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