In a uniform circular motion, the centripetal acceleration is

Options

A. Towards the centre of the circular path and perpendicular to the instantaneous velocity
B. Away from the centre of the circular path and perpendicular to the instantaneous velocity
C. A variable acceleration making `45^@` with the instantaneous velocity
D. A variable acceleration , parallel to the instantaneous velocity

Answer

To solve the question regarding centripetal acceleration in uniform circular motion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Uniform Circular Motion**:
- In uniform circular motion, an object moves in a circular path with a constant speed. Although the speed is constant, the direction of the velocity vector changes continuously as the object moves along the circular path.

2. **Defining Centripetal Acceleration**:
- Centripetal acceleration is the acceleration that acts on an object moving in a circular path, directed towards the center of the circle. It is responsible for changing the direction of the velocity vector, keeping the object in circular motion.

3. **Formula for Centripetal Acceleration**:
- The formula for centripetal acceleration (\(a_c\)) is given by:
\[ a_c = \frac{v^2}{r} \]
where \(v\) is the constant speed of the object and \(r\) is the radius of the circular path.

4. **Direction of Centripetal Acceleration**:
- The direction of centripetal acceleration is always towards the center of the circular path. This means that it is perpendicular to the instantaneous velocity of the object at any point in its motion.

5. **Conclusion**:
- In uniform circular motion, the centripetal acceleration is constant in magnitude (as both \(v\) and \(r\) are constant) and is directed towards the center of the circle.

### Final Answer:
In a uniform circular motion, the centripetal acceleration is directed towards the center of the circular path and is given by the formula \(a_c = \frac{v^2}{r}\).

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