A body is whirled in a horizontal circle of radius `20cm`. It has an angular velocity of `10rad//s`. What is its linear velocity at any point on the circular path

Options

A. `10m//s`
B. `2m//s`
C. `20m//s`
D. `sqrt(2)m//s`

Answer

To find the linear velocity of a body moving in a circular path, we can use the relationship between linear velocity (v), angular velocity (ω), and the radius (r) of the circular path. The formula is given by:

\[ v = r \cdot \omega \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Radius (r) = 20 cm = 0.2 m (convert cm to m)
- Angular velocity (ω) = 10 rad/s

2. **Substitute the values into the formula:**
\[ v = r \cdot \omega \]
\[ v = 0.2 \, \text{m} \cdot 10 \, \text{rad/s} \]

3. **Calculate the linear velocity:**
\[ v = 2 \, \text{m/s} \]

4. **Conclusion:**
The linear velocity of the body at any point on the circular path is **2 m/s**.