Consider the motion of the tip of the minute hand of a clock. In one hour

Options

A. the displacement is zero
B. the distance covered is zero
C. the average speed is zero
D. the average velocity is zero

Answer

To solve the problem regarding the motion of the tip of the minute hand of a clock in one hour, we will follow these steps:

### Step 1: Understand the motion of the minute hand
The minute hand of a clock completes one full revolution in one hour. This means that it returns to its initial position after one hour.

### Step 2: Determine the displacement
Displacement is defined as the shortest distance from the initial position to the final position. Since the minute hand returns to its original position after one hour, the initial and final positions are the same.

- **Displacement** = Final Position - Initial Position = 0

### Step 3: Calculate the distance covered
Distance is the total length of the path traveled by the minute hand. The minute hand moves in a circular path, and the distance covered in one complete revolution is the circumference of the circle.

- **Distance covered** = Circumference of the circle = \(2 \pi r\), where \(r\) is the length of the minute hand.

### Step 4: Calculate average velocity
Average velocity is defined as the total displacement divided by the total time taken. Since the displacement is 0:

- **Average Velocity** = Total Displacement / Total Time = 0 / 1 hour = 0

### Step 5: Calculate average speed
Average speed is defined as the total distance covered divided by the total time taken. The total distance covered is \(2 \pi r\) and the total time is 1 hour:

- **Average Speed** = Total Distance / Total Time = \(2 \pi r / 1\) hour = \(2 \pi r\)

### Conclusion
- Displacement = 0
- Distance covered = \(2 \pi r\)
- Average Velocity = 0
- Average Speed = \(2 \pi r\)

Thus, the correct answers are that the displacement is 0 and the average velocity is 0, while the distance covered is \(2 \pi r\) and the average speed is \(2 \pi r\).