Calculate the speed of the tip of second's hand of a watch of length `1.5 cm`.

Options

A. `0.16 cm//s`
B. `0.12 cm//s`
C. 1 cm/s
D. None

Explanation

To calculate the speed of the tip of the second's hand of a watch with a length of 1.5 cm, follow these steps:

### Step-by-Step Solution:

1. **Identify the given information:**
- Length of the second's hand (L) = 1.5 cm

2. **Understand the motion of the second's hand:**
- The second's hand completes one full revolution in 60 seconds.

3. **Calculate the circumference of the circle traced by the tip of the second's hand:**
- The circumference (C) of a circle is given by the formula \( C = 2\pi r \), where \( r \) is the radius.
- Here, the radius \( r \) is the length of the second's hand, which is 1.5 cm.
\[ C = 2\pi \times 1.5 \text{ cm} \]
\[ C = 3\pi \text{ cm} \]

4. **Determine the time taken for one full revolution:**
- The second's hand takes 60 seconds to complete one full revolution.

5. **Calculate the speed of the tip of the second's hand:**
- Speed is defined as the distance traveled divided by the time taken.
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- Here, the distance traveled in one full revolution is the circumference \( C \), and the time taken is 60 seconds.
\[ \text{Speed} = \frac{3\pi \text{ cm}}{60 \text{ s}} \]
\[ \text{Speed} = \frac{\pi \times 1.5 \text{ cm}}{30 \text{ s}} \]
\[ \text{Speed} = \frac{1.5\pi}{30} \text{ cm/s} \]
\[ \text{Speed} = \frac{\pi}{20} \text{ cm/s} \]

6. **Approximate the value of \(\pi\) (if needed):**
- Using \(\pi \approx 3.14159\),
\[ \text{Speed} \approx \frac{3.14159}{20} \text{ cm/s} \]
\[ \text{Speed} \approx 0.157 \text{ cm/s} \]

### Final Answer:
The speed of the tip of the second's hand is approximately \( 0.157 \text{ cm/s} \).