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 along a circular path with a constant speed. However, its direction changes continuously.

2. **Identifying the Type of Acceleration**:
- The only acceleration present in uniform circular motion is centripetal acceleration. This acceleration is responsible for changing the direction of the object's velocity while maintaining its speed.

3. **Direction of Centripetal Acceleration**:
- Centripetal acceleration always points towards the center of the circular path. This is crucial because it is what keeps the object moving in a circular trajectory.

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

5. **Characteristics of Centripetal Acceleration**:
- Centripetal acceleration does not change the speed of the object; it only changes the direction of the velocity vector. Therefore, it is always perpendicular to the instantaneous velocity of the object.

6. **Conclusion**:
- In summary, in uniform circular motion, the centripetal acceleration is directed towards the center of the circular path, is responsible for changing the direction of the velocity, and its magnitude can be calculated using the formula \(a_c = \frac{v^2}{r}\).