For a particle performing uniform circular motion, choose the incorrect statement form the following.

Options

A. Magnitude of particle velocity (speed) remains constant.
B. Particle velocity remains directed perpendicular to radius vector.
C. Direction of acceleration keeps changing as particle moves.
D. Magnitudes of acceleration does not remain constant.

Explanation

To solve the question regarding the incorrect statement for a particle performing uniform circular motion, we will analyze each statement provided:

1. **Magnitude of particle velocity (i.e., speed) remains constant.**
- In uniform circular motion, the speed of the particle is constant. Although the direction of the velocity changes, the magnitude (speed) does not. This statement is **correct**.

2. **Particle velocity remains directed perpendicular to the radius vector.**
- In uniform circular motion, the velocity vector is always tangent to the circular path. The radius vector points from the center of the circle to the particle, and at every point, the velocity is indeed perpendicular to the radius vector. This statement is **correct**.

3. **Direction of acceleration keeps changing as the particle moves.**
- In uniform circular motion, the acceleration (centripetal acceleration) is always directed towards the center of the circle. As the particle moves around the circle, the direction of this acceleration does change, but it always points towards the center. This statement is **correct**.

4. **Magnitudes of acceleration do not remain constant.**
- In uniform circular motion, while the direction of the acceleration changes, the magnitude of the centripetal acceleration remains constant. The magnitude of acceleration is given by \( a = \frac{v^2}{r} \), where \( v \) is the constant speed and \( r \) is the radius of the circle. Therefore, this statement is **incorrect**.

Based on the analysis above, the incorrect statement is:

**Answer: Magnitudes of acceleration do not remain constant.**