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. `-1.2 ` MJ
B. `-8.0` MJ
C. `-16 MJ`
D. `-2.4 ` MJ

Answer

To find the potential energy of a satellite revolving around the Earth, we can use the relationship between kinetic energy and potential energy in the context of gravitational forces. Here’s a step-by-step solution:

### Step 1: Understand the relationship between kinetic and potential energy
The potential energy (U) of a satellite in orbit is related to its kinetic energy (K) by the formula:
\[ U = -2K \]

### Step 2: Calculate the kinetic energy of the satellite
The kinetic energy (K) of an object can be calculated using the formula:
\[ K = \frac{1}{2} m v^2 \]
where:
- \( m \) is the mass of the satellite,
- \( v \) is the speed of the satellite.

Given:
- Mass of the satellite, \( m = 400 \, \text{kg} \)
- Speed of the satellite, \( v = 200 \, \text{m/s} \)

Substituting the values into the kinetic energy formula:
\[ K = \frac{1}{2} \times 400 \, \text{kg} \times (200 \, \text{m/s})^2 \]

### Step 3: Calculate the value of kinetic energy
Calculating \( (200 \, \text{m/s})^2 \):
\[ (200)^2 = 40000 \, \text{m}^2/\text{s}^2 \]

Now substituting this back into the kinetic energy formula:
\[ K = \frac{1}{2} \times 400 \times 40000 \]
\[ K = 200 \times 40000 \]
\[ K = 8000000 \, \text{J} \]
\[ K = 8 \times 10^6 \, \text{J} \]

### Step 4: Calculate the potential energy
Using the relationship \( U = -2K \):
\[ U = -2 \times 8 \times 10^6 \, \text{J} \]
\[ U = -16 \times 10^6 \, \text{J} \]
\[ U = -16 \, \text{MJ} \]

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