For a particle performing a uniform circular motion the acceleration is

Options

A. constant in direction
B. constant in magnitude but not in direction
C. constant in magnitude and direction
D. constant neither in magnitude nor in direction.

Answer

To solve the question regarding the acceleration of a particle performing uniform circular motion, let's break down the concepts step by step.

### Step-by-Step Solution:

1. **Understanding Uniform Circular Motion**:
- In uniform circular motion, a particle moves in a circular path with a constant speed. This means that while the speed (the magnitude of velocity) remains constant, the direction of the velocity vector changes continuously.

**Hint**: Remember that uniform circular motion implies constant speed but changing direction.

2. **Acceleration in Circular Motion**:
- Acceleration is defined as the rate of change of velocity. Since the velocity is a vector quantity, any change in its direction (even if the speed remains constant) results in acceleration.

**Hint**: Acceleration occurs whenever there is a change in velocity, which includes changes in direction.

3. **Direction of Acceleration**:
- In uniform circular motion, the acceleration is directed towards the center of the circular path. This is known as centripetal acceleration. The formula for centripetal acceleration (a_c) is given by:
\[ a_c = \frac{v^2}{r} \]
where \( v \) is the constant speed and \( r \) is the radius of the circular path.

**Hint**: Remember that centripetal acceleration always points towards the center of the circle.

4. **Magnitude of Acceleration**:
- The magnitude of the centripetal acceleration remains constant as long as the speed and radius of the circular path do not change. Therefore, the acceleration has a constant magnitude.

**Hint**: The magnitude of acceleration in uniform circular motion is constant as long as speed and radius are unchanged.

5. **Conclusion**:
- In summary, for a particle performing uniform circular motion, the acceleration is constant in magnitude but not in direction. The direction of the acceleration continuously changes as the particle moves around the circular path, always pointing towards the center.

**Final Statement**: The acceleration of a particle in uniform circular motion is constant in magnitude but varies in direction.