A particle is moving on a circular path with constant speed, then its acceleration will be constant in

Options

A. magnitude
B. direction
C. both magnitude and direction
D. neither magnitude nor direction

Answer

To solve the question, we need to analyze the motion of a particle moving in a circular path with constant speed.

### Step-by-Step Solution:

1. **Understanding Circular Motion**:
- A particle moving in a circular path is undergoing circular motion. In this case, the particle is moving with a constant speed, which means that the magnitude of its velocity is constant.

2. **Identifying Types of Acceleration**:
- In circular motion, there are two types of acceleration to consider:
- **Centripetal Acceleration (Ac)**: This is directed towards the center of the circular path and is responsible for changing the direction of the velocity vector, keeping the particle in circular motion.
- **Tangential Acceleration (At)**: This is responsible for changing the speed of the particle along the circular path.

3. **Analyzing the Given Condition**:
- Since the particle is moving with a constant speed, it implies that there is no tangential acceleration (At = 0). This means that the speed of the particle does not change.

4. **Centripetal Acceleration**:
- The centripetal acceleration (Ac) is given by the formula:
\[ A_c = \frac{v^2}{r} \]
where \( v \) is the constant speed of the particle and \( r \) is the radius of the circular path.
- Since both \( v \) and \( r \) are constant, the magnitude of the centripetal acceleration remains constant.

5. **Direction of Acceleration**:
- Although the magnitude of centripetal acceleration is constant, its direction is not constant. It continuously changes as the particle moves along the circular path, always pointing towards the center of the circle.

6. **Conclusion**:
- Therefore, while the magnitude of the centripetal acceleration remains constant, its direction changes continuously. Thus, the overall acceleration of the particle is not constant due to the changing direction of the centripetal acceleration.

### Final Answer:
The acceleration of a particle moving in a circular path with constant speed is not constant because the direction of the centripetal acceleration changes, even though its magnitude remains constant.