Consider the motion of the tip of the minute hand of a clock. In one hour
(a) the displacement is zero
(b) the distance covered is zero
(c) the average speed is zero
(d) the average velocity is zero

Options

A. a & b are correct
B. a, b & c are correct
C. a & d are correct
D. b,c & d are correct

Answer

To analyze the motion of the tip of the minute hand of a clock over one hour, we need to understand the concepts of displacement, distance, average speed, and average velocity.

### Step-by-Step Solution:

1. **Understanding Displacement**:
- Displacement is defined as the shortest distance from the initial position to the final position, along with the direction.
- In one hour, the minute hand moves from the 12 o'clock position back to the 12 o'clock position. Therefore, the initial and final positions are the same.
- **Displacement = Final Position - Initial Position = 0**.

2. **Understanding Distance Covered**:
- Distance covered is the total path length traveled by the minute hand.
- The minute hand completes a full circle in one hour. The circumference of the circle can be calculated using the formula \(C = 2\pi r\), where \(r\) is the radius (length of the minute hand).
- Thus, the distance covered in one hour is equal to the circumference of the circle traced by the minute hand.
- **Distance Covered = Circumference = \(2\pi r\)** (which is not zero).

3. **Understanding Average Speed**:
- Average speed is defined as the total distance traveled divided by the total time taken.
- Since the minute hand covers a distance equal to the circumference of the circle in one hour, the average speed can be calculated as:
- **Average Speed = Total Distance / Total Time = \(2\pi r / 1\) hour** (which is not zero).

4. **Understanding Average Velocity**:
- Average velocity is defined as the displacement divided by the total time taken.
- Since the displacement is zero (as established in step 1), the average velocity will also be zero.
- **Average Velocity = Displacement / Total Time = 0 / 1 hour = 0**.

### Conclusion:
- (a) The displacement is zero: **True**.
- (b) The distance covered is zero: **False**.
- (c) The average speed is zero: **False**.
- (d) The average velocity is zero: **True**.

### Final Answer:
The correct options are (a) and (d).