A satellite of mass 50 kg moves from a point where the gravitational potential due to the Earth is `-20MNkg^(-1)` to another point where the gravitational potential is `-60MJkg^(-1)`.During the change of position, it has moved

Options

A. Close to the Earth and lost 2000 MJ of potential energy
B. Closer to the Earth and lost 20 MJ of potential energy
C. Farther from the Earth and gained 2000 MJ of potential energy
D. Farther from the Earth and gained 40 MJ of potential energy

Answer

To solve the problem, we need to determine the change in gravitational potential energy of the satellite as it moves from one point to another.

### Step-by-Step Solution:

1. **Identify the initial and final gravitational potentials**:
- Initial gravitational potential, \( V_i = -20 \, \text{MJ/kg} \)
- Final gravitational potential, \( V_f = -60 \, \text{MJ/kg} \)

2. **Calculate the change in gravitational potential**:
- The change in gravitational potential, \( \Delta V \), is given by:
\[ \Delta V = V_f - V_i \]
- Substituting the values:
\[ \Delta V = (-60 \, \text{MJ/kg}) - (-20 \, \text{MJ/kg}) = -60 + 20 = -40 \, \text{MJ/kg} \]

3. **Calculate the change in gravitational potential energy**:
- The change in gravitational potential energy \( \Delta U \) can be calculated using the formula:
\[ \Delta U = m \cdot \Delta V \]
- Where \( m \) is the mass of the satellite (50 kg):
\[ \Delta U = 50 \, \text{kg} \cdot (-40 \, \text{MJ/kg}) = -2000 \, \text{MJ} \]

4. **Interpret the result**:
- The negative sign indicates that the gravitational potential energy of the satellite has decreased by 2000 MJ as it moved closer to the Earth.

### Final Answer:
The change in gravitational potential energy of the satellite is **-2000 MJ**.