For a particle performing uniform circular motion , choose the correct statement (s) from the following :

Options

A. Magnitude of particle velocity (speed) remains constant
B. Particle velocity remains directed perpendicular to radius vector
C. Direction of acceleration keeps changing as particle moves .
D. Angular momentum is constant in magnitude but direction keeps changing .

Explanation

To analyze the statements regarding a particle performing uniform circular motion, we will evaluate each statement based on the principles of circular motion.

### Step-by-Step Solution:

1. **Understanding Uniform Circular Motion**:
- A particle in uniform circular motion travels along a circular path with a constant speed. However, its velocity changes due to the continuous change in direction. The acceleration is directed towards the center of the circle.

2. **Evaluating Statement 1**:
- **Statement**: "Magnitude of a particle's velocity (speed) remains constant."
- **Analysis**: In uniform circular motion, the speed (magnitude of velocity) is constant. Therefore, this statement is **correct**.

3. **Evaluating Statement 2**:
- **Statement**: "Particle velocity remains directed perpendicular to the radius vector."
- **Analysis**: In circular motion, the velocity vector is always tangent to the circular path, while the radius vector points from the center to the particle. Thus, the velocity is indeed perpendicular to the radius vector. This statement is **correct**.

4. **Evaluating Statement 3**:
- **Statement**: "Direction of acceleration keeps changing as the particle moves."
- **Analysis**: The centripetal acceleration is always directed towards the center of the circle. As the particle moves, the direction of this acceleration changes, even though its magnitude remains constant. Therefore, this statement is **correct**.

5. **Evaluating Statement 4**:
- **Statement**: "Angular momentum is constant in magnitude, but the direction keeps changing."
- **Analysis**: The angular momentum \( L \) of a particle is given by \( L = m \cdot r \cdot v \). If we consider the angular momentum about the center of the circle, both \( r \) and \( v \) are perpendicular and constant in magnitude, thus making the angular momentum constant in magnitude and direction. However, if we consider points not at the center, the angular momentum can vary. Therefore, this statement is **incorrect**.

### Conclusion:
The correct statements regarding a particle performing uniform circular motion are:
- Statement 1: Correct
- Statement 2: Correct
- Statement 3: Correct
- Statement 4: Incorrect

Thus, the correct options are **1, 2, and 3**.

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