A body mass 100 g is revolving in a horizontal circle. If its frequency of rotation is 3.5 r.p.s. and radius of circular path is 0.5 m, the angular speed of the body is

Options

A. 18 `rad//s`
B. 20`rad//s`
C. 22`rad//s`
D. 24`rad//s`

Answer

To find the angular speed of a body revolving in a horizontal circle, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the body, \( m = 100 \, \text{g} = 0.1 \, \text{kg} \) (conversion from grams to kilograms)
- Frequency of rotation, \( f = 3.5 \, \text{r.p.s.} \)
- Radius of the circular path, \( r = 0.5 \, \text{m} \)

2. **Understand the Relationship Between Frequency and Angular Speed:**
- The angular speed \( \omega \) (in radians per second) can be calculated using the formula:
\[ \omega = 2\pi f \]
- Here, \( f \) is the frequency in revolutions per second.

3. **Substitute the Given Frequency into the Formula:**
- Plugging in the value of \( f \):
\[ \omega = 2\pi \times 3.5 \]

4. **Calculate the Angular Speed:**
- First, calculate \( 2 \times 3.5 = 7 \):
\[ \omega = 7\pi \]
- Now, using the approximate value of \( \pi \approx 3.14 \):
\[ \omega \approx 7 \times 3.14 = 21.98 \, \text{rad/s} \]

5. **Round Off the Result:**
- Rounding \( 21.98 \, \text{rad/s} \) gives approximately:
\[ \omega \approx 22 \, \text{rad/s} \]

6. **Conclusion:**
- Therefore, the angular speed of the body is \( 22 \, \text{rad/s} \).

### Final Answer:
The angular speed of the body is \( 22 \, \text{rad/s} \).

---