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

Options

A. it velocity is constant
B. its acceleration is constant
C. its kinetic energy is constant
D. it moves in a circular path

Answer

To solve the problem, we need to analyze the motion of a particle subjected to a force that is always perpendicular to its velocity. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Force and Motion
The problem states that a particle is acted upon by a force of constant magnitude that is always perpendicular to its velocity. This means that the direction of the force is always at a right angle to the direction of motion.

**Hint:** Recall that when a force is perpendicular to the direction of motion, it does not do work on the particle.

### Step 2: Analyze Work Done by the Force
Since the force is perpendicular to the velocity, the work done (W) by the force can be calculated using the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \( \theta \) is the angle between the force and the displacement. Here, \( \theta = 90^\circ \), so:
\[ W = F \cdot d \cdot \cos(90^\circ) = 0 \]
This indicates that the work done by the force is zero.

**Hint:** Remember that work done is related to the change in kinetic energy of the particle.

### Step 3: Apply the Work-Energy Theorem
According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy:
\[ W = \Delta KE \]
Since the work done is zero, we have:
\[ \Delta KE = 0 \]
This means that the kinetic energy of the particle remains constant.

**Hint:** Kinetic energy is given by the formula \( KE = \frac{1}{2}mv^2 \). If it is constant, then the speed of the particle must also be constant.

### Step 4: Determine the Nature of Motion
Since the force is always perpendicular to the velocity and the kinetic energy is constant, the particle will not speed up or slow down. Instead, the force acts as a centripetal force, causing the particle to change direction while maintaining a constant speed.

**Hint:** Think about the nature of circular motion and how centripetal force works.

### Step 5: Conclude the Motion
The conclusion is that the particle moves in a circular path with constant speed due to the constant perpendicular force acting on it.

**Final Answer:**
1. The kinetic energy of the particle remains constant.
2. The particle moves in a circular path.