Length of clocks second hands 0.1 m what is the order of its angular velocity in radian per/sec.

Options

A. `10^(-1)`
B. `10^(-2)`
C. `10^(-3)`
D. `10^(-4)`

Answer

To find the order of the angular velocity of a clock's second hand with a length of 0.1 m, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Angular Velocity**:
Angular velocity (ω) is defined as the angle (θ) covered per unit time (t). The formula for angular velocity is:
\[ \omega = \frac{\theta}{t} \]

2. **Determine the Angular Displacement**:
For one complete revolution, the angular displacement (θ) is:
\[ \theta = 2\pi \text{ radians} \]

3. **Determine the Time Period**:
The time taken for one complete revolution of the second hand is:
\[ t = 60 \text{ seconds} \]

4. **Calculate Angular Velocity**:
Substituting the values of θ and t into the angular velocity formula:
\[ \omega = \frac{2\pi}{60} \]

5. **Simplify the Expression**:
Simplifying the expression gives:
\[ \omega = \frac{\pi}{30} \text{ radians per second} \]

6. **Express in Order of Magnitude**:
To express this in terms of order, we can approximate π as 3.14:
\[ \omega \approx \frac{3.14}{30} \approx 0.10467 \text{ radians per second} \]
This can be expressed in scientific notation as:
\[ \omega \approx 10^{-1} \text{ radians per second} \]

7. **Conclusion**:
The order of the angular velocity is:
\[ 10^{-1} \text{ radians per second} \]