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

Answer

To find the linear velocity of a body whirling in a horizontal circle, we can use the relationship between linear velocity (v), angular velocity (ω), and the radius (r) of the circle.

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius of the circle, \( r = 20 \, \text{cm} = 0.2 \, \text{m} \) (conversion from cm to m)
- Angular velocity, \( \omega = 10 \, \text{rad/s} \)

2. **Use the formula for linear velocity**:
The linear velocity \( v \) of an object moving in a circular path can be calculated using the formula:
\[ v = \omega \times r \]

3. **Substitute the known values into the formula**:
\[ v = 10 \, \text{rad/s} \times 0.2 \, \text{m} \]

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

5. **Conclusion**:
The linear velocity of the body at any point on the circular path is \( 2 \, \text{m/s} \).

### Final Answer:
The linear velocity at any point on the circular path is \( 2 \, \text{m/s} \).

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