A particle is moving in a curved path. Which of the following quantities may remain constant during its motion?

Options

A. Acceleration
B. Velocity
C. Magnitude of acceleration
D. None of these

Explanation

To determine which quantities may remain constant during the motion of a particle moving in a curved path, we can analyze the nature of the quantities involved.

### Step-by-Step Solution:

1. **Understanding Motion in a Curved Path**:
- A particle moving in a curved path experiences changes in both direction and magnitude of its velocity. This is due to the continuous change in direction as the particle follows the curve.

2. **Acceleration**:
- Acceleration is a vector quantity that has both magnitude and direction. As the particle moves along the curved path, the direction of acceleration changes at different points of the path. Therefore, the acceleration does not remain constant.
- **Conclusion**: Acceleration does not remain constant.

3. **Velocity**:
- Velocity is also a vector quantity. Similar to acceleration, the direction of velocity changes as the particle moves along the curve. Hence, the velocity does not remain constant.
- **Conclusion**: Velocity does not remain constant.

4. **Magnitude of Acceleration**:
- While the direction of acceleration changes, it is possible for the magnitude of acceleration to remain constant if the particle moves with uniform acceleration. In some cases, the particle may experience a constant centripetal acceleration while moving along a circular path.
- **Conclusion**: The magnitude of acceleration may remain constant.

5. **Other Quantities**:
- Other quantities such as kinetic energy may also change if the speed of the particle changes. However, if the particle moves with constant speed along the curved path, kinetic energy remains constant.

### Final Conclusion:
- The quantity that may remain constant during the motion of a particle moving in a curved path is the **magnitude of acceleration** (if it is uniform).