If linear speed of a particle moving in a circular path is constant then,angular speed is proportional to (r is radius of circle)

Options

A. 1/r
B. `1/r^2`
C. `1/r^3`
D. `r^0`

Answer

To solve the question, we need to establish the relationship between linear speed (V), angular speed (ω), and the radius (r) of the circular path.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The linear speed (V) of a particle moving in a circular path is related to its angular speed (ω) and the radius (r) of the circle by the formula:
\[ V = r \cdot \omega \]

2. **Given Condition**:
The problem states that the linear speed (V) is constant. This means that as the particle moves, its linear speed does not change.

3. **Rearranging the Formula**:
Since V is constant, we can rearrange the equation to express angular speed (ω) in terms of linear speed (V) and radius (r):
\[ \omega = \frac{V}{r} \]

4. **Analyzing the Relationship**:
From the rearranged equation, we can see that if V is constant, then the angular speed (ω) is inversely proportional to the radius (r):
\[ \omega \propto \frac{1}{r} \]

5. **Conclusion**:
Therefore, if the linear speed of a particle moving in a circular path is constant, the angular speed is inversely proportional to the radius of the circle.

### Final Answer:
The angular speed (ω) is inversely proportional to the radius (r) of the circle.

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