If the kinetic energy of a satellite is `2xx10^(4)J`, then its potential energy will be

Options

A. `-2xx10^(-4)J`
B. `4xx10^(4)J`
C. `-4xx10^(4)J`
D. `-10^(4)J`

Explanation

To find the potential energy of a satellite given its kinetic energy, we can use the relationship between kinetic energy (KE) and potential energy (PE) in the context of gravitational fields.

### Step-by-Step Solution:

1. **Identify the given data:**
- Kinetic Energy (KE) of the satellite = \(2 \times 10^4 \, \text{J}\)

2. **Recall the relationship between kinetic energy and potential energy for a satellite:**
- The kinetic energy of a satellite in orbit is given by the formula:
\[ KE = \frac{G M m}{2R} \]
- The potential energy (PE) of the satellite is given by:
\[ PE = -\frac{G M m}{R} \]

3. **Establish the relationship between KE and PE:**
- From the formulas, we can derive that:
\[ PE = -2 \times KE \]
- This means that the potential energy is negative and twice the kinetic energy.

4. **Calculate the potential energy:**
- Substitute the value of kinetic energy into the equation for potential energy:
\[ PE = -2 \times (2 \times 10^4 \, \text{J}) = -4 \times 10^4 \, \text{J} \]

5. **Final result:**
- Therefore, the potential energy of the satellite is:
\[ PE = -4 \times 10^4 \, \text{J} \]

### Summary:
The potential energy of the satellite is \(-4 \times 10^4 \, \text{J}\).

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