If the length of second's hand of a clock is 10 cm, the speed of its dip (in cm 1s^(-1)`) is nearly

Options

A. 2
B. `0.5`
C. `1.5`
D. 1

Explanation

To find the speed of the tip of the second hand of a clock, we can follow these steps:

### Step 1: Understand the motion of the second hand
The second hand of a clock moves in a circular path. The speed of the tip of the second hand can be calculated using the formula for linear speed in circular motion.

### Step 2: Identify the radius
The length of the second hand is given as 10 cm. This length acts as the radius (r) of the circular path traced by the tip of the second hand.

### Step 3: Calculate the angular velocity
The angular velocity (ω) of the second hand can be calculated as follows:
- The second hand completes one full rotation (2π radians) in 60 seconds.
- Therefore, the angular velocity is:
\[ \omega = \frac{2\pi \text{ radians}}{60 \text{ seconds}} = \frac{\pi}{30} \text{ radians/second} \]

### Step 4: Use the formula for linear speed
The linear speed (V) of the tip of the second hand can be calculated using the formula:
\[ V = r \cdot \omega \]
Where:
- \( r = 10 \text{ cm} \)
- \( \omega = \frac{\pi}{30} \text{ radians/second} \)

Substituting the values:
\[ V = 10 \text{ cm} \cdot \frac{\pi}{30} \text{ radians/second} \]

### Step 5: Simplify the expression
Now, we can simplify the expression:
\[ V = \frac{10\pi}{30} \text{ cm/second} = \frac{\pi}{3} \text{ cm/second} \]

### Step 6: Approximate the value
Using the approximation \( \pi \approx 3.14 \):
\[ V \approx \frac{3.14}{3} \text{ cm/second} \approx 1.05 \text{ cm/second} \]

### Final Answer
Thus, the speed of the tip of the second hand is approximately **1 cm/s**.

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