The angular separation between the minute hand and hour hand of a clock at 12.20pm is

Options

A. `120^(@)`
B. `90^(@)`
C. `110^(@)`
D. `100^(@)`

Answer

To find the angular separation between the minute hand and the hour hand of a clock at 12:20 PM, we can follow these steps:

### Step 1: Understand the movement of the hands
- The minute hand completes a full circle (360 degrees) in 60 minutes.
- The hour hand completes a full circle (360 degrees) in 12 hours.

### Step 2: Calculate the angular speed of each hand
- **Minute Hand:**
- In 60 minutes, it travels 360 degrees.
- Therefore, in 1 minute, it travels:
\[ \text{Minute hand speed} = \frac{360 \text{ degrees}}{60 \text{ minutes}} = 6 \text{ degrees per minute} \]

- **Hour Hand:**
- In 12 hours, it travels 360 degrees.
- Therefore, in 1 hour (60 minutes), it travels:
\[ \text{Hour hand speed} = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees per hour} \]
- In 1 minute, it travels:
\[ \text{Hour hand speed} = \frac{30 \text{ degrees}}{60 \text{ minutes}} = 0.5 \text{ degrees per minute} \]

### Step 3: Calculate the positions of the hands at 12:20 PM
- **Minute Hand Position:**
- At 20 minutes past the hour, the minute hand has moved:
\[ \text{Minute hand position} = 20 \text{ minutes} \times 6 \text{ degrees/minute} = 120 \text{ degrees} \]

- **Hour Hand Position:**
- At 12:20 PM, the hour hand has moved:
\[ \text{Hour hand position} = 20 \text{ minutes} \times 0.5 \text{ degrees/minute} = 10 \text{ degrees} \]

### Step 4: Calculate the angular separation
- The angular separation between the two hands is the absolute difference between their positions:
\[ \text{Angular separation} = |120 \text{ degrees} - 10 \text{ degrees}| = 110 \text{ degrees} \]

### Final Answer
Thus, the angular separation between the minute hand and the hour hand at 12:20 PM is **110 degrees**.

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