Two particles A and B are moving in uniform circular motion in concentric circles of radii `r_(A)` and `r_(B)` with speed `u_(A)` and `u_(B)` respectively. Their time period of rotation is the same. The ratio of angular speed of a to that of B will be:

Options

A. `1:1`
B. `r_(A):r_(B)`
C. `upsilon_(A):upsilon_(B)`
D. `r_(B):r_(A)`

Explanation

To solve the problem, we need to find the ratio of the angular speeds of two particles A and B that are moving in uniform circular motion.

### Step-by-Step Solution:

1. **Understanding Angular Speed**:
The angular speed (ω) of an object in circular motion is given by the formula:
\[ \omega = \frac{2\pi}{T} \]
where \( T \) is the time period of rotation.

2. **Given Information**:
- Both particles A and B have the same time period of rotation, which means:
\[ T_A = T_B \]
- The angular speeds for particles A and B can be expressed as:
\[ \omega_A = \frac{2\pi}{T_A} \]
\[ \omega_B = \frac{2\pi}{T_B} \]

3. **Finding the Ratio of Angular Speeds**:
We need to find the ratio of the angular speed of A to that of B:
\[ \frac{\omega_A}{\omega_B} = \frac{\frac{2\pi}{T_A}}{\frac{2\pi}{T_B}} \]
Here, the \( 2\pi \) terms cancel out:
\[ \frac{\omega_A}{\omega_B} = \frac{T_B}{T_A} \]

4. **Substituting the Time Periods**:
Since \( T_A = T_B \), we can substitute:
\[ \frac{\omega_A}{\omega_B} = \frac{T_B}{T_A} = \frac{T_A}{T_A} = 1 \]

5. **Conclusion**:
Therefore, the ratio of the angular speed of A to that of B is:
\[ \frac{\omega_A}{\omega_B} = 1 \]

### Final Answer:
The ratio of angular speed of A to that of B is \( 1:1 \).