When a body moves in a circle, the work done by the centripetal forces is always

Options

A. `gt 0`
B. `lt 0`
C. Zero
D. Minimum

Answer

To solve the question regarding the work done by centripetal forces when a body moves in a circle, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Centripetal Force**:
- Centripetal force is the force that acts on an object moving in a circular path, directed towards the center of the circle.

2. **Work Done by a Force**:
- The work done (W) by a force is given by the formula:
\[ W = F \cdot s \cdot \cos(\theta) \]
where \( F \) is the magnitude of the force, \( s \) is the displacement, and \( \theta \) is the angle between the force and the displacement vector.

3. **Direction of Centripetal Force**:
- In circular motion, the centripetal force is always directed towards the center of the circle.

4. **Displacement in Circular Motion**:
- As the body moves in a circular path, the displacement at any point is tangential to the circle.

5. **Angle Between Force and Displacement**:
- Since the centripetal force is directed towards the center and the displacement is tangential, the angle \( \theta \) between the centripetal force and the displacement is \( 90^\circ \).

6. **Calculating Work Done**:
- Substituting \( \theta = 90^\circ \) into the work formula:
\[ W = F \cdot s \cdot \cos(90^\circ) \]
- Since \( \cos(90^\circ) = 0 \):
\[ W = F \cdot s \cdot 0 = 0 \]

7. **Conclusion**:
- Therefore, the work done by the centripetal force when a body moves in a circle is always **zero**.

### Final Answer:
The work done by the centripetal forces is always **zero**.