A particle revolves round a circular path with a constant speed.
(i) the velecity of the particle is along the tangent.
(ii) the acceleration of the particle of the particle is always towards center.
(iii) the magnetic of acceleration is constant.
(iv) The work done by the centripetal force is always zero.

Options

A. `(i),(ii)`
B. `(i),(ii),(iii)`
C. `(ii),(iii),(iv)`
D. All options are correct

Answer

To analyze the statements given in the question about a particle revolving in a circular path with constant speed, we will evaluate each statement step by step.

### Step-by-Step Solution:

1. **Understanding Circular Motion**:
- A particle moving in a circular path with constant speed is undergoing uniform circular motion. In this type of motion, the speed (magnitude of velocity) remains constant, but the direction of the velocity vector changes continuously.

2. **Evaluating Statement (i)**:
- **Statement**: The velocity of the particle is along the tangent.
- **Explanation**: In circular motion, the velocity vector is always tangent to the circular path at any point. Therefore, this statement is **true**.

3. **Evaluating Statement (ii)**:
- **Statement**: The acceleration of the particle is always towards the center.
- **Explanation**: In uniform circular motion, the only acceleration present is the centripetal acceleration, which is directed towards the center of the circular path. Hence, this statement is also **true**.

4. **Evaluating Statement (iii)**:
- **Statement**: The magnitude of acceleration is constant.
- **Explanation**: The centripetal acceleration \( a_c \) is given by the formula \( a_c = \frac{v^2}{r} \), where \( v \) is the constant speed and \( r \) is the radius of the circular path. Since both \( v \) and \( r \) are constant, the magnitude of centripetal acceleration remains constant. Thus, this statement is **true**.

5. **Evaluating Statement (iv)**:
- **Statement**: The work done by the centripetal force is always zero.
- **Explanation**: The work done by a force is calculated as \( W = F \cdot d \cdot \cos(\theta) \), where \( \theta \) is the angle between the force and the direction of displacement. In uniform circular motion, the centripetal force is always directed towards the center (90 degrees to the direction of motion), so \( \cos(90^\circ) = 0 \). Therefore, the work done by the centripetal force is indeed **zero**. This statement is **true**.

### Conclusion:
All four statements are correct.