A body is moving in a circular path with a constant speed. It has .

Options

A. (a)constant velocity
B. (b)constant momentum
C. (c)constant kinetic energy
D. (d)constant acceleration

Explanation

To solve the problem step by step, we can analyze the motion of a body moving in a circular path with constant speed.

### Step 1: Understand the Motion
A body moving in a circular path with constant speed means that the magnitude of its velocity remains the same, but the direction of the velocity vector changes continuously.

**Hint:** Remember that speed is a scalar quantity, while velocity is a vector quantity that includes both magnitude and direction.

### Step 2: Analyze Velocity
Since the body is moving in a circular path, the direction of the velocity vector changes at every point along the path. Therefore, even though the speed is constant, the velocity is not constant because the direction is changing.

**Hint:** Consider how the direction of the velocity vector changes as the object moves around the circle.

### Step 3: Analyze Momentum
Momentum (P) is given by the formula \( P = mv \), where \( m \) is mass and \( v \) is velocity. Since the velocity is not constant (due to changing direction), the momentum of the body is also not constant.

**Hint:** Recall that momentum is a vector quantity and depends on both the magnitude and direction of velocity.

### Step 4: Analyze Acceleration
Acceleration is defined as the rate of change of velocity with respect to time. Since the velocity is changing (even though the speed is constant), the body experiences centripetal acceleration directed towards the center of the circular path. Thus, the acceleration is also not constant.

**Hint:** Consider how acceleration behaves in circular motion, especially the concept of centripetal acceleration.

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

**Hint:** Remember that kinetic energy depends only on the speed (magnitude) and not on the direction of motion.

### Conclusion
Based on the analysis:
- Velocity is not constant.
- Momentum is not constant.
- Acceleration is not constant.
- Kinetic energy is constant.

Thus, the correct answer is that the kinetic energy remains constant while the body moves in a circular path with constant speed.

**Final Answer:** Kinetic energy is constant.