Two identical satellite are at `R` and `7R` away from earth surface, the wrong statement is (`R`=radius of earth)

Options

A. Ratio of total energy of both is5
B. ratio of kinetic energy of both is 4
C. ratio of potential energy of both 4
D. ratio of total energy of both is 4 and ratio of magnitude fo potential to kinetic energy is 2.

Explanation

To solve the question regarding the two identical satellites at distances \( R \) and \( 7R \) from the Earth's surface, we need to analyze the gravitational forces, kinetic energy, potential energy, and their relationships. Let's break this down step by step.

### Step 1: Determine the distances from the center of the Earth
The radius of the Earth is denoted as \( R \). Therefore, the distances of the satellites from the center of the Earth are:
- For the first satellite at distance \( R \) from the surface:
\[ d_1 = R + R = 2R \]
- For the second satellite at distance \( 7R \) from the surface:
\[ d_2 = R + 7R = 8R \]

### Step 2: Write the expressions for gravitational force
The gravitational force acting on a satellite is given by Newton's law of gravitation:
\[ F = \frac{GMm}{d^2} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, \( m \) is the mass of the satellite, and \( d \) is the distance from the center of the Earth.

For the two satellites, we have:
- For the first satellite:
\[ F_1 = \frac{GMm}{(2R)^2} = \frac{GMm}{4R^2} \]
- For the second satellite:
\[ F_2 = \frac{GMm}{(8R)^2} = \frac{GMm}{64R^2} \]

### Step 3: Determine the kinetic energy
The kinetic energy \( K \) of a satellite in orbit can be expressed in terms of gravitational force:
\[ K = \frac{1}{2}mv^2 \]
From the gravitational force, we know that:
\[ F = m \frac{v^2}{d} \implies v^2 = \frac{F \cdot d}{m} \]
Thus, substituting for \( F \):
\[ K = \frac{1}{2} m \left( \frac{GMm}{d^2} \cdot d \right) = \frac{GMm}{2d} \]
Calculating for both satellites:
- For the first satellite:
\[ K_1 = \frac{GMm}{2 \cdot 2R} = \frac{GMm}{4R} \]
- For the second satellite:
\[ K_2 = \frac{GMm}{2 \cdot 8R} = \frac{GMm}{16R} \]

### Step 4: Determine the potential energy
The potential energy \( U \) of a satellite is given by:
\[ U = -\frac{GMm}{d} \]
Calculating for both satellites:
- For the first satellite:
\[ U_1 = -\frac{GMm}{2R} \]
- For the second satellite:
\[ U_2 = -\frac{GMm}{8R} \]

### Step 5: Analyze the ratios of energies
We can now analyze the ratios of potential energy to kinetic energy for both satellites:
- For the first satellite:
\[ \text{Magnitude of } \frac{U_1}{K_1} = \frac{-\frac{GMm}{2R}}{\frac{GMm}{4R}} = -2 \]
- For the second satellite:
\[ \text{Magnitude of } \frac{U_2}{K_2} = \frac{-\frac{GMm}{8R}}{\frac{GMm}{16R}} = -2 \]

### Conclusion
The analysis shows that the ratios of potential energy to kinetic energy for both satellites are the same. The statement that might be wrong could relate to the relationship between these energies or the distances involved.

### Final Answer
The wrong statement is likely one that misrepresents the relationship between the energies or distances of the satellites.