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

Options

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

Answer

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 Movement of the Hour Hand**:
The hour hand of a clock completes one full rotation (360 degrees) in 12 hours.

2. **Convert Time from Hours to Seconds**:
Since we need the angular speed in degrees per second, we first convert 12 hours into seconds.
\[ 12 \text{ hours} = 12 \times 60 \text{ minutes} \times 60 \text{ seconds} = 12 \times 3600 \text{ seconds} = 43200 \text{ seconds} \]

3. **Calculate Angular Speed**:
Angular speed (ω) is defined as the total angular displacement divided by the total time taken. Therefore, we can use the formula:
\[ \omega = \frac{\text{Total Angular Displacement}}{\text{Total Time}} = \frac{360 \text{ degrees}}{43200 \text{ seconds}} \]

4. **Simplify the Calculation**:
Now, we simplify the fraction:
\[ \omega = \frac{360}{43200} \]
To simplify, we can divide both the numerator and the denominator by 360:
\[ \omega = \frac{1}{120} \text{ degrees per second} \]

5. **Final Answer**:
Thus, the angular speed of the hour hand of a clock is:
\[ \omega = \frac{1}{120} \text{ degrees per second} \]