A particle is revolving in a circle with increasing its speed uniformly. Which of the following is constant ?

Options

A. Centripetal acceleration
B. Tangential acceleration
C. Angular acceleration
D. None of these

Explanation

To solve the question, "A particle is revolving in a circle with increasing its speed uniformly. Which of the following is constant?" we will analyze the different types of acceleration involved in circular motion and determine which one remains constant.

### Step-by-Step Solution:

1. **Understanding Circular Motion**:
- A particle moving in a circle experiences centripetal acceleration directed towards the center of the circle and tangential acceleration directed along the tangent to the circle.

2. **Centripetal Acceleration**:
- The formula for centripetal acceleration (\(a_c\)) is given by:
\[ a_c = \frac{v^2}{R} \]
where \(v\) is the linear speed of the particle and \(R\) is the radius of the circle.
- Since the speed \(v\) is increasing uniformly, \(a_c\) will also increase as \(v\) increases. Therefore, centripetal acceleration is **not constant**.

3. **Tangential Acceleration**:
- Tangential acceleration (\(a_t\)) is related to the change in speed along the circular path. It can be expressed as:
\[ a_t = \alpha \cdot R \]
where \(\alpha\) is the angular acceleration.
- Since the speed is increasing uniformly, \(a_t\) will also change as the speed changes. Thus, tangential acceleration is **not constant**.

4. **Angular Acceleration**:
- Angular acceleration (\(\alpha\)) is defined as the rate of change of angular velocity (\(\omega\)) with respect to time:
\[ \alpha = \frac{d\omega}{dt} \]
- Given that the speed is increasing uniformly, the angular velocity \(\omega\) also increases uniformly. Therefore, \(\alpha\) remains constant.

5. **Conclusion**:
- Among the options provided, the only acceleration that remains constant is the **angular acceleration** (\(\alpha\)). Thus, the correct answer is option 3.

### Final Answer:
**Angular acceleration is constant.**

---