Angular speed of the hour of a clock in degree per second is

Options

A. `(1)/(30)`
B. `(1)/(60)`
C. `(1)/(120)`
D. `(1)/(720)`

Explanation

To find the angular speed of the hour hand of a clock in degrees per second, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the angular speed (ω) of the hour hand of a clock in degrees per second. The hour hand completes one full revolution (360 degrees) in 12 hours.

2. **Identify the Total Angle Covered**: The hour hand covers a total angle of 360 degrees in one complete cycle (12 hours).

3. **Determine the Time Period**: The time period for one complete cycle of the hour hand is 12 hours.

4. **Convert Time Period to Seconds**:
- 1 hour = 60 minutes
- 1 minute = 60 seconds
- Therefore, 12 hours = 12 × 60 minutes = 720 minutes
- And, 720 minutes = 720 × 60 seconds = 43200 seconds.

5. **Calculate Angular Speed**:
- The formula for angular speed (ω) is given by:
\[ ω = \frac{\text{Total Angle}}{\text{Time Period}} \]
- Substituting the values:
\[ ω = \frac{360 \text{ degrees}}{43200 \text{ seconds}} \]

6. **Simplify the Expression**:
- Calculate the value:
\[ ω = \frac{360}{43200} = \frac{1}{120} \text{ degrees per second} \]

7. **Final Result**: The angular speed of the hour hand of a clock is:
\[ ω = \frac{1}{120} \text{ degrees per second} \]

### Conclusion:
The answer to the question is \(\frac{1}{120}\) degrees per second.

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