The K.E. of a satellite is 2MJ. Its total energy is

Options

A. `-0.5` MJ
B. `-2` MJ
C. `-1` MJ
D. `-4` MJ

Answer

To solve the problem, we need to find the total energy of a satellite given its kinetic energy. Here’s the step-by-step solution:

### Step 1: Understand the relationship between kinetic energy and total energy of a satellite.
For a satellite in orbit, the total energy (E) is related to its kinetic energy (K.E) and potential energy (P.E) as follows:
\[ E = K.E + P.E \]

### Step 2: Recall the formulas for kinetic energy and potential energy.
The kinetic energy of a satellite is given by:
\[ K.E = \frac{G M m}{2r} \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the Earth,
- \( m \) is the mass of the satellite,
- \( r \) is the distance from the center of the Earth to the satellite.

The potential energy (P.E) of the satellite is given by:
\[ P.E = -\frac{G M m}{r} \]

### Step 3: Substitute the kinetic energy into the total energy equation.
From the problem, we know that the kinetic energy of the satellite is \( K.E = 2 \, \text{MJ} = 2 \times 10^6 \, \text{J} \).

Using the relationship between kinetic energy and potential energy, we can express the total energy:
\[ E = K.E + P.E \]
Since the potential energy is twice the negative of the kinetic energy:
\[ P.E = -2 \times K.E \]

### Step 4: Calculate the total energy.
Substituting the value of kinetic energy into the potential energy formula:
\[ P.E = -2 \times (2 \times 10^6) = -4 \times 10^6 \, \text{J} \]

Now substituting back into the total energy equation:
\[ E = K.E + P.E \]
\[ E = (2 \times 10^6) + (-4 \times 10^6) \]
\[ E = 2 \times 10^6 - 4 \times 10^6 \]
\[ E = -2 \times 10^6 \, \text{J} \]

### Conclusion:
The total energy of the satellite is:
\[ E = -2 \, \text{MJ} \]