If a satellite of mass 400 kg revolves around the earth in an orbit with speed 200 m/s then its potential energy is

Options

A. -16MJ
B. -8MJ
C. -4MJ
D. -32MJ

Answer

To find the potential energy of a satellite revolving around the Earth, we can follow these steps:

### Step 1: Understand the formulas
The potential energy (U) of a satellite in orbit is given by the formula:
\[ U = -\frac{G M m}{r} \]
where:
- \( G \) is the gravitational constant (\( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)),
- \( M \) is the mass of the Earth (\( 5.972 \times 10^{24} \, \text{kg} \)),
- \( m \) is the mass of the satellite (400 kg),
- \( r \) is the distance from the center of the Earth to the satellite.

### Step 2: Relate kinetic energy to potential energy
The kinetic energy (KE) of the satellite is given by:
\[ KE = \frac{1}{2} m v^2 \]
where \( v \) is the speed of the satellite (200 m/s).

From the relationship between kinetic energy and potential energy, we know:
\[ U = -2 \times KE \]

### Step 3: Calculate the kinetic energy
Substituting the values into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 400 \, \text{kg} \times (200 \, \text{m/s})^2 \]
\[ KE = \frac{1}{2} \times 400 \times 40000 \]
\[ KE = 200 \times 40000 \]
\[ KE = 8000000 \, \text{J} \]
or
\[ KE = 8 \, \text{MJ} \]

### Step 4: Calculate the potential energy
Now, using the relationship \( U = -2 \times KE \):
\[ U = -2 \times 8 \, \text{MJ} \]
\[ U = -16 \, \text{MJ} \]

### Conclusion
The potential energy of the satellite is:
\[ U = -16 \, \text{MJ} \]