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 problem of a particle revolving in a circle while increasing its speed uniformly, we will analyze the different quantities involved in circular motion.

### Step-by-Step Solution:

1. **Understanding the Motion**:
The particle is moving in a circular path and its speed is increasing uniformly. This means that the particle has both tangential and centripetal accelerations.

2. **Centripetal Acceleration**:
Centripetal acceleration (\(a_c\)) is given by the formula:
\[ a_c = \frac{v^2}{R} \]
where \(v\) is the speed of the particle and \(R\) is the radius of the circle. Since the speed \(v\) is increasing, the centripetal acceleration will also change and thus is not constant.

**Hint**: Remember that centripetal acceleration depends on the square of the speed.

3. **Tangential Acceleration**:
Tangential acceleration (\(a_t\)) is defined as the rate of change of speed:
\[ a_t = \frac{dv}{dt} \]
Since the problem states that the speed is increasing uniformly, this means that \(dv/dt\) is constant. However, the direction of the tangential acceleration changes as the particle moves along the circular path.

**Hint**: Uniform increase in speed means constant tangential acceleration, but its direction varies.

4. **Angular Acceleration**:
Angular acceleration (\(\alpha\)) is related to tangential acceleration and radius by the formula:
\[ \alpha = \frac{a_t}{R} \]
Since \(a_t\) is constant (as established earlier) and \(R\) is constant, the angular acceleration will also be constant.

**Hint**: Angular acceleration is constant when tangential acceleration is constant and radius does not change.

5. **Conclusion**:
From the analysis, we conclude that the only quantity that remains constant in this scenario is the angular acceleration. Therefore, the correct answer is that angular acceleration is constant.

### Final Answer:
The quantity that is constant is **angular acceleration**.