A constant force is acting perpendicular to the velocity of a particle. For this situation, which one of the following is correct?

Options

A. Velocity is constant
B. Acceleration is constant
C. Momentum will be constant
D. The particle follows an elliptical path

Explanation

To solve the question, we need to analyze the situation where a constant force is acting perpendicular to the velocity of a particle. Let's break it down step by step.

### Step 1: Understanding the Forces and Motion
When a constant force acts perpendicular to the velocity of a particle, it does not change the magnitude of the velocity (speed) but changes its direction. This is a key point because it indicates that the particle will not speed up or slow down but will change its path.

**Hint:** Remember that a force acting perpendicular to the direction of motion influences only the direction of the velocity, not its magnitude.

### Step 2: Circular Motion
A force that is always perpendicular to the velocity will cause the particle to move in a circular path. This is because the force continuously changes the direction of the velocity vector, keeping the particle in circular motion.

**Hint:** Think about how a string pulls a ball in a circle; the tension in the string acts perpendicular to the ball's velocity at every point.

### Step 3: Analyzing Velocity and Momentum
Since the direction of the velocity is changing, the velocity vector itself is changing even if the speed remains constant. Therefore, the momentum, which is the product of mass and velocity, will also change because momentum is a vector quantity.

**Hint:** Recall that momentum is defined as \( p = mv \), where \( v \) is the velocity vector. If the direction of \( v \) changes, \( p \) changes too.

### Step 4: Acceleration Consideration
The acceleration of the particle, which is directed towards the center of the circular path (centripetal acceleration), will also change direction as the particle moves. Although the magnitude of the centripetal acceleration can remain constant (if the speed is constant), its direction is always changing.

**Hint:** Remember that acceleration is also a vector quantity, and its direction matters.

### Step 5: Conclusion
Given the above analysis, we can conclude that:
- The particle will follow a circular path due to the perpendicular force.
- The speed remains constant, but the velocity changes due to direction changes.
- Momentum is not constant because the velocity vector is changing.
- The acceleration is not constant in the long term due to its changing direction.

Thus, the correct answer to the question is that the particle follows a circular path.

### Final Answer:
The particle follows a circular path.