Which of the following statements is corrent ?

Options

A. The net acceleration of a particle in circular motion is always towards the centre of the circle
B. The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point
C. The acceleration vector of a particle in circular path have constant acceleration
D. It is not possible to revolve a particle in circular path with constant acceleration.

Answer

To solve the question regarding which statements about motion in a circular path are correct, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Analyzing Statement 1**:
- The statement claims that the net acceleration of a particle in circular motion is always towards the center of the circle.
- In circular motion, a particle experiences centripetal acceleration directed towards the center of the circle. However, if there is tangential acceleration (due to a change in speed), the net acceleration will not point directly towards the center but will be a vector sum of centripetal and tangential accelerations.
- **Conclusion**: This statement is **false**.

2. **Analyzing Statement 2**:
- The statement claims that the velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.
- In circular motion, the velocity of the particle is always tangent to the circular path at any given point. This is a fundamental property of motion along a curved path.
- **Conclusion**: This statement is **true**.

3. **Analyzing Statement 3**:
- The statement claims that the acceleration vector of a particle in a circular path has constant acceleration.
- In circular motion, while the magnitude of the centripetal acceleration can remain constant if the speed is constant, the direction of the acceleration vector continuously changes as the particle moves along the circular path. Therefore, the acceleration vector is not constant.
- **Conclusion**: This statement is **false**.

4. **Analyzing Statement 4**:
- The statement claims that it is not possible to revolve a particle in a circular path with constant acceleration.
- This statement is somewhat misleading. A particle can revolve in a circular path with constant centripetal acceleration if it moves with constant speed. However, if we consider total acceleration (which includes tangential acceleration), then for constant speed, the tangential acceleration must be zero, leading to a constant centripetal acceleration. Thus, the statement can be interpreted as true in the context of total acceleration.
- **Conclusion**: This statement is **true**.

### Final Results:
- **Correct Statements**: Statement 2 and Statement 4.
- **Incorrect Statements**: Statement 1 and Statement 3.