The minute hand of a clock Is 10 cm long. The linear speed of its tip Is

Options

A. `1.643xx10^(-4)ms^(-1)`
B. `1.876xx10^(-4)ms^(-1)`
C. `1.744xx10^(-4)ms^(-1)`
D. `1.502xx10^(-4)ms^(-1)`

Explanation

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

### Step 1: Identify the Length of the Minute Hand
The length of the minute hand is given as 10 cm. We need to convert this to meters for our calculations.
- **Conversion**:
\[ \text{Length in meters} = \frac{10 \text{ cm}}{100} = 0.1 \text{ m} \]

### Step 2: Determine the Time Period of the Minute Hand
The minute hand completes one full revolution in 60 minutes. We need to convert this time into seconds.
- **Conversion**:
\[ \text{Time period} = 60 \text{ minutes} \times 60 \text{ seconds/minute} = 3600 \text{ seconds} \]

### Step 3: Calculate Angular Velocity (ω)
The angular velocity (ω) can be calculated using the formula:
\[ \omega = \frac{2\pi}{\text{Time period}} \]
Substituting the time period we found:
\[ \omega = \frac{2\pi}{3600 \text{ seconds}} \approx 1.745 \times 10^{-3} \text{ rad/s} \]

### Step 4: Calculate Linear Speed (v)
The linear speed (v) of the tip of the minute hand can be calculated using the formula:
\[ v = r \cdot \omega \]
Where \( r \) is the radius (length of the minute hand) and \( \omega \) is the angular velocity.
Substituting the values:
\[ v = 0.1 \text{ m} \cdot 1.745 \times 10^{-3} \text{ rad/s} \approx 1.745 \times 10^{-4} \text{ m/s} \]

### Final Answer
The linear speed of the tip of the minute hand is approximately:
\[ v \approx 1.745 \times 10^{-4} \text{ m/s} \]