Work done by centripetal force in revolving a satellite around the earth is

Options

A. zero
B. unity
C. infinity
D. nothing can be decided

Explanation

To determine the work done by the centripetal force in revolving a satellite around the Earth, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Centripetal Force**:
- A satellite in orbit around the Earth experiences a centripetal force that keeps it in circular motion. This force is provided by the gravitational attraction between the Earth and the satellite.

2. **Identifying the Forces**:
- The gravitational force acting on the satellite can be expressed as:
\[ F = \frac{G \cdot M \cdot m}{r^2} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, \( m \) is the mass of the satellite, and \( r \) is the distance from the center of the Earth to the satellite.

3. **Direction of Forces**:
- The gravitational force acts towards the center of the Earth, which is also the direction of the centripetal force required for circular motion.

4. **Motion of the Satellite**:
- The satellite moves in a circular path, and its velocity is tangential to the circular orbit at any point. The direction of the velocity is always perpendicular to the direction of the centripetal force.

5. **Calculating Work Done**:
- Work done (\( W \)) by a force is given by the formula:
\[ W = F \cdot s \cdot \cos(\theta) \]
where \( \theta \) is the angle between the force and the displacement.
- In the case of the satellite, the centripetal force (gravitational force) is always perpendicular to the displacement of the satellite. Therefore, \( \theta = 90^\circ \).

6. **Applying the Cosine Function**:
- Since \( \cos(90^\circ) = 0 \), the work done by the centripetal force is:
\[ W = F \cdot s \cdot \cos(90^\circ) = F \cdot s \cdot 0 = 0 \]

7. **Conclusion**:
- The work done by the centripetal force in revolving a satellite around the Earth is **zero**.

### Final Answer:
The work done by the centripetal force in revolving a satellite around the Earth is **zero**.