If the length of second`s hand in a clock is 4 cm,the angular velocity and linear velocity of the tip is

Options

A. `pi/30 rad s^-1,pi/750m/s`
B. `pi/6 rad s^-1,pi/1500m/s`
C. `pi/15 rad s^-1,pi/375m/s`
D. `pi/12 rads^-1,pi/350m/s`

Answer

To find the angular velocity and linear velocity of the tip of the second's hand in a clock, we can follow these steps:

### Step 1: Identify the Length of the Second's Hand
The length of the second's hand is given as 4 cm.

### Step 2: Convert Length to Meters
To work with standard SI units, we convert the length from centimeters to meters:
\[ 4 \text{ cm} = \frac{4}{100} \text{ m} = 0.04 \text{ m} \]

### Step 3: Calculate Angular Velocity
The angular velocity (\(\omega\)) of the second's hand can be calculated using the formula:
\[ \omega = \frac{\text{Angle}}{\text{Time}} \]
The second's hand completes one full revolution (which is \(2\pi\) radians) in 60 seconds. Therefore:
\[ \omega = \frac{2\pi \text{ radians}}{60 \text{ seconds}} = \frac{\pi}{30} \text{ radians/second} \]

### Step 4: Calculate Linear Velocity
The linear velocity (\(v\)) of the tip of the second's hand can be calculated using the formula:
\[ v = \omega \times r \]
where \(r\) is the radius (length of the second's hand). Substituting the values we have:
\[ v = \left(\frac{\pi}{30} \text{ radians/second}\right) \times (0.04 \text{ m}) \]
\[ v = \frac{\pi \times 0.04}{30} \text{ m/s} \]
\[ v = \frac{\pi}{750} \text{ m/s} \]

### Final Answers
- **Angular Velocity (\(\omega\))**: \(\frac{\pi}{30} \text{ radians/second}\)
- **Linear Velocity (\(v\))**: \(\frac{\pi}{750} \text{ m/s}\)

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