If a particle is moving on circular path with uniform speed,then which of the following physical quantity remains constant?

Options

A. Acceleration
B. Kinetic energy
C. Momentum
D. Velocity

Answer

To determine which physical quantity remains constant when a particle is moving on a circular path with uniform speed, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding Uniform Speed**:
- Uniform speed means that the magnitude of the velocity (speed) of the particle remains constant throughout its motion. However, the direction of the velocity changes continuously as the particle moves along the circular path.

**Hint**: Remember that speed is a scalar quantity, while velocity is a vector quantity that includes both magnitude and direction.

2. **Analyzing Velocity**:
- Since the particle is moving in a circular path, even though the speed is constant, the direction of the velocity vector changes at every point on the path. Therefore, the velocity itself is not constant.

**Hint**: Consider how velocity is defined and how direction affects it.

3. **Considering Momentum**:
- Momentum (p) is defined as the product of mass (m) and velocity (v): \( p = m \cdot v \). Since the velocity is changing (due to the changing direction), the momentum will also change.

**Hint**: Recall that momentum is also a vector quantity, and both magnitude and direction are important.

4. **Kinetic Energy**:
- Kinetic energy (KE) is given by the formula: \( KE = \frac{1}{2} mv^2 \). Since the mass (m) is constant and the speed (the magnitude of velocity) is constant, the kinetic energy remains constant.

**Hint**: Focus on the relationship between speed and kinetic energy, and remember that only the magnitude of velocity affects kinetic energy.

5. **Acceleration**:
- The acceleration of the particle is directed towards the center of the circular path (centripetal acceleration). Since the direction of velocity is changing, the acceleration is also changing as it continuously points towards the center.

**Hint**: Think about how acceleration is related to changes in velocity and the direction of motion.

6. **Conclusion**:
- The only physical quantity that remains constant while the particle moves in a circular path with uniform speed is the kinetic energy.

### Final Answer:
The physical quantity that remains constant is **Kinetic Energy**.