When a body moves with a constant speed along a circle

Options

A. No work is done on it
B. No acceleration is produced in it
C. Its velocity remains constant
D. No force acts on it

Answer

### Step-by-Step Solution:

1. **Understanding the Motion**:
- When a body moves in a circular path with a constant speed, it is undergoing uniform circular motion. The speed remains constant, but the direction of the velocity vector changes continuously.

2. **Identifying Forces**:
- In uniform circular motion, the body experiences a centripetal force directed towards the center of the circle. This force is responsible for changing the direction of the velocity vector, keeping the body in circular motion.

3. **Analyzing Work Done**:
- Work done (W) is calculated using the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \(F\) is the force, \(d\) is the displacement, and \(\theta\) is the angle between the force and displacement vectors.

4. **Direction of Forces and Displacement**:
- In circular motion, the centripetal force acts radially inward, while the displacement of the body is tangential to the circle. This means that the angle \(\theta\) between the centripetal force and the displacement is 90 degrees.

5. **Calculating Work Done**:
- Since \(\theta = 90^\circ\), we have:
\[ \cos(90^\circ) = 0 \]
Therefore, the work done is:
\[ W = F \cdot d \cdot 0 = 0 \]
- This indicates that no work is done on the body as it moves along the circular path.

6. **Conclusion**:
- Although the body is moving with constant speed, the direction of its velocity is changing, which means its velocity vector is not constant. However, since no work is done on the body, its kinetic energy remains constant.

### Final Answer:
- The work done on the body is zero, and while the speed is constant, the velocity is not constant due to the change in direction.