The hour hand and the minute hand of a clock coincide at every relative peridic time is ,

Options

A. `11//12 hour`
B. `12//11 hour`
C. `11//6 hour`
D. `12//24 hour`

Explanation

To solve the problem of how often the hour hand and the minute hand of a clock coincide, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Movement of the Hands**:
- The hour hand completes one full rotation (360 degrees) in 12 hours.
- The minute hand completes one full rotation in 1 hour.

2. **Calculating Angular Speeds**:
- The angular speed of the hour hand, \( \omega_H \), is given by:
\[ \omega_H = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees/hour} \]
- The angular speed of the minute hand, \( \omega_M \), is:
\[ \omega_M = \frac{360 \text{ degrees}}{1 \text{ hour}} = 360 \text{ degrees/hour} \]

3. **Relative Angular Speed**:
- When considering the relative motion, we can think of the minute hand as stationary. The relative angular speed of the hour hand with respect to the minute hand is:
\[ \omega_{\text{relative}} = \omega_M - \omega_H = 360 \text{ degrees/hour} - 30 \text{ degrees/hour} = 330 \text{ degrees/hour} \]

4. **Finding the Time Period for Coincidence**:
- The hands coincide when the hour hand completes a full rotation relative to the minute hand. This occurs when the hour hand moves through 360 degrees relative to the minute hand.
- The time taken for this to happen can be calculated using:
\[ T = \frac{\text{Total angle}}{\text{Relative angular speed}} = \frac{360 \text{ degrees}}{330 \text{ degrees/hour}} = \frac{360}{330} \text{ hours} = \frac{12}{11} \text{ hours} \]

5. **Conclusion**:
- Therefore, the hour hand and the minute hand of a clock coincide every \( \frac{12}{11} \) hours.

### Final Answer:
The hour hand and the minute hand of a clock coincide every \( \frac{12}{11} \) hours.

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