Two satellites A and B move round the earth in the same orbit. The mass of B is twice the mass of A.

Options

A. Speeds of A and B are equal
B. The potential energy of earth +A is same is that of earth +B
C. The kinetic energy of A and B are equal
D. The total energy of earth +A is same as that of earth +B

Answer

To solve the problem, we need to analyze the motion of the two satellites A and B around the Earth. Let's break down the solution step by step:

### Step 1: Understand the problem
We have two satellites, A and B, that are orbiting the Earth in the same orbit. The mass of satellite B is twice that of satellite A. We need to analyze their speeds, potential energy, kinetic energy, and total energy.

### Step 2: Determine the speed of the satellites
The speed \( v \) of a satellite in orbit is given by the formula:
\[ v = \sqrt{\frac{GM}{r}} \]
where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth,
- \( r \) is the radius of the orbit (distance from the center of the Earth to the satellite).

Since both satellites A and B are in the same orbit, they have the same radius \( r \). Therefore, their speeds will be:
\[ v_A = \sqrt{\frac{GM}{r}} \quad \text{and} \quad v_B = \sqrt{\frac{GM}{r}} \]
This shows that the speeds of satellites A and B are equal:
\[ v_A = v_B \]

### Step 3: Analyze the potential energy
The gravitational potential energy \( U \) of a satellite in orbit is given by:
\[ U = -\frac{GMm}{r} \]
For satellite A, the potential energy \( U_A \) is:
\[ U_A = -\frac{G M m_A}{r} \]
For satellite B, the potential energy \( U_B \) is:
\[ U_B = -\frac{G M m_B}{r} = -\frac{G M (2m_A)}{r} = -\frac{2G M m_A}{r} \]
Thus, the potential energy of satellite B is not equal to that of satellite A.

### Step 4: Analyze the kinetic energy
The kinetic energy \( KE \) of a satellite is given by:
\[ KE = \frac{1}{2} mv^2 \]
For satellite A, the kinetic energy \( KE_A \) is:
\[ KE_A = \frac{1}{2} m_A v_A^2 \]
For satellite B, the kinetic energy \( KE_B \) is:
\[ KE_B = \frac{1}{2} m_B v_B^2 = \frac{1}{2} (2m_A) v_B^2 = m_A v_B^2 \]
Since \( v_A = v_B \), we have:
\[ KE_B = m_A v_A^2 \]
This shows that the kinetic energies of A and B are not equal.

### Step 5: Analyze the total energy
The total energy \( E \) of a satellite in orbit is given by:
\[ E = KE + U \]
For satellite A:
\[ E_A = KE_A + U_A = \frac{1}{2} m_A v_A^2 - \frac{G M m_A}{r} \]
For satellite B:
\[ E_B = KE_B + U_B = m_A v_B^2 - \frac{2G M m_A}{r} \]
Since both kinetic and potential energies depend on the mass, the total energies will also differ.

### Conclusion
From the analysis:
- The speeds of satellites A and B are equal.
- The potential energies of A and B are not equal.
- The kinetic energies of A and B are not equal.
- The total energies of A and B are not equal.

Thus, the correct answer is that the speeds of A and B are equal.