A clock has it's minute-hand `10 cm` long. Find the average velocity between `6.00 AM` to `6.30AM` for the tip of minute-hand.

Options

A. `(22)/(21)cmm i n^(-1)`
B. `(2)/(21)cm mi n^(-1)`
C. `(12)/(21)cm mi n^(-1)`
D. `(2)/(3)cmmi n^(-1)`

Explanation

To find the average velocity of the tip of the minute hand of a clock from 6:00 AM to 6:30 AM, we can follow these steps:

### Step 1: Understand the motion of the minute hand
The minute hand of the clock moves in a circular path. At 6:00 AM, the minute hand points at the 12 (or 0 degrees), and at 6:30 AM, it points at the 6 (or 180 degrees).

### Step 2: Calculate the displacement
Displacement is defined as the shortest distance from the initial position to the final position. In this case, the minute hand moves from the 12 to the 6, which is a straight line through the center of the clock.

- The length of the minute hand is given as 10 cm.
- The displacement can be calculated as the straight line distance between the two points (12 and 6 on the clock). This forms a straight line that is the diameter of the circle traced by the minute hand.

Using the formula for the diameter of a circle:
\[ \text{Displacement} = 2 \times \text{radius} = 2 \times 10 \text{ cm} = 20 \text{ cm} \]

### Step 3: Calculate the time taken
The time taken from 6:00 AM to 6:30 AM is:
\[ \text{Time} = 30 \text{ minutes} \]

### Step 4: Calculate the average velocity
Average velocity is defined as the total displacement divided by the total time taken. Thus:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{20 \text{ cm}}{30 \text{ minutes}} = \frac{2}{3} \text{ cm/min} \]

### Final Answer
The average velocity of the tip of the minute hand from 6:00 AM to 6:30 AM is:
\[ \frac{2}{3} \text{ cm/min} \]