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 solve the question regarding the motion of the tip of the minute hand of a clock, we need to analyze the concepts of displacement, distance, average speed, and average velocity.

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

**Hint:** Consider the definition of displacement and how it relates to the starting and ending positions of an object.

### Step 2: Calculate the displacement
Displacement is defined as the change in position of an object. Since the minute hand returns to its original position after one hour, the initial and final positions are the same. Thus, the displacement is zero.

**Hint:** Recall that displacement is a vector quantity that depends on the initial and final positions.

### Step 3: Calculate the distance covered
The distance covered by the minute hand is the length of the path it travels. In one hour, the minute hand travels along the circumference of the clock. The distance covered can be calculated using the formula for the circumference of a circle, which is \(2\pi R\), where \(R\) is the length of the minute hand.

**Hint:** Remember that distance is a scalar quantity and does not depend on the direction of motion.

### Step 4: Calculate the average speed
Average speed is defined as the total distance traveled divided by the total time taken. Since the distance covered is \(2\pi R\) and the time taken is 1 hour, the average speed is non-zero.

**Hint:** Average speed is calculated using the formula: \( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \).

### Step 5: Calculate the average velocity
Average velocity is defined as the total displacement divided by the total time taken. Since the displacement is zero (as established in Step 2), the average velocity is also zero.

**Hint:** Average velocity is a vector quantity and is affected by the displacement, which is zero in this case.

### Conclusion
Based on the analysis:
- The displacement is zero.
- The distance covered is \(2\pi R\) (non-zero).
- The average speed is non-zero (since it is the distance divided by time).
- The average velocity is zero (since it is the displacement divided by time).

Thus, the correct options are:
- 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**

The correct answers are options A and D.

### Final Answer:
- The correct options are A (The displacement is zero) and D (The average velocity is zero).