A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that

Options

A. (a)Velocity is constant
B. (b)Acceleration is constant
C. (c)Kinetic energy is constant
D. (d)It moves in a circular path

Explanation

To solve the problem, we need to analyze the motion of a particle acted upon by a force of constant magnitude that is always perpendicular to its velocity. Let's break down the solution step by step:

### Step 1: Understanding the Force and Motion
When a force acts on a particle and is always perpendicular to its velocity, it means that the force does not do any work on the particle. This is because work done is given by the dot product of force and displacement, and if the force is perpendicular to the velocity, the work done is zero.

**Hint:** Recall that work done is zero when the force is perpendicular to the direction of motion.

### Step 2: Circular Motion
Since the force is always perpendicular to the velocity, it continuously changes the direction of the velocity vector. This is characteristic of uniform circular motion. Therefore, the particle will move in a circular path.

**Hint:** Think about how centripetal force acts on an object moving in a circle.

### Step 3: Analyzing Velocity
In circular motion, while the direction of the velocity changes, the magnitude of the velocity (speed) remains constant. This means that the particle's speed does not change, but its direction does.

**Hint:** Consider how the speed of an object moving in a circle remains constant while its direction changes.

### Step 4: Analyzing Acceleration
The acceleration of the particle is directed towards the center of the circular path (centripetal acceleration). Although the magnitude of this acceleration can be constant, the direction of the acceleration changes continuously as the particle moves along the circular path. Thus, the acceleration is not constant.

**Hint:** Remember that acceleration is a vector quantity and depends on both magnitude and direction.

### Step 5: Kinetic Energy
The kinetic energy of the particle is given by the formula \( KE = \frac{1}{2} mv^2 \). Since the speed (magnitude of velocity) remains constant, the kinetic energy of the particle also remains constant.

**Hint:** Kinetic energy depends only on the speed, not the direction of motion.

### Conclusion
Based on the analysis:
- The particle follows a circular path (Option D is correct).
- The velocity changes direction but not magnitude (implying velocity is not constant).
- The acceleration is not constant due to changing direction.
- The kinetic energy remains constant (Option C is correct).

### Final Answer
The correct options are C and D.