Which of the following sets of concurrent force may be in equilibrium?

Options

A. Velocity vector is parallel to position vector
B. Velocity vector is perpendicular to position vector
C. Acceleration vector is directed towards the origin
D. Acceleration vector is directed away from the origin

Explanation

To determine which sets of concurrent forces may be in equilibrium, we will analyze the conditions for equilibrium in the context of the given options.

### Step-by-Step Solution:

1. **Understanding Equilibrium**:
- For a set of concurrent forces to be in equilibrium, the net force acting on the body must be zero. This implies that the acceleration of the body must also be zero (Newton's First Law of Motion).

2. **Analyzing the First Option**:
- The first option states that the velocity vector is parallel to the position vector.
- If the velocity is constant and parallel to the position vector, it means that there is no change in the direction of motion. Therefore, the acceleration (which is the change in velocity over time) is zero.
- Since acceleration is zero, the net force acting on the body is also zero. Thus, the concurrent forces in this case may be in equilibrium.

3. **Analyzing the Second Option**:
- The second option states that the velocity vector is perpendicular to the position vector.
- In this scenario, if the velocity vector is perpendicular to the position vector, the direction of the velocity is changing continuously as the particle moves. This implies that there is a net acceleration present (since acceleration is the rate of change of velocity).
- Since there is a net acceleration, the net force acting on the body is not zero, and therefore, the concurrent forces cannot be in equilibrium.

4. **Analyzing the Third and Fourth Options**:
- Both options C and D also imply scenarios where there is some form of acceleration present.
- Similar to the second option, if there is acceleration, it indicates that the net force acting on the body is not zero.
- Consequently, the concurrent forces in these cases cannot be in equilibrium either.

### Conclusion:
- The only set of concurrent forces that may be in equilibrium is the first option where the velocity vector is parallel to the position vector.