The circular orbit of two satellites have radii `r_(1)` and `r_(2)` respectively `(r_(1)ltr_(2))`. If angular velosities of satellites are same, then their centripetal accelerations are related as

Options

A. `a_(1)gta_(2)`
B. `a_(1)=a_(2)`
C. `a_(1)lta_(2)`
D. Data insufficient

Explanation

To solve the problem, we need to relate the centripetal accelerations of two satellites in circular orbits with different radii but the same angular velocity. Let's denote the centripetal accelerations of the satellites as \( A_1 \) for the satellite with radius \( r_1 \) and \( A_2 \) for the satellite with radius \( r_2 \).

### Step-by-Step Solution:

1. **Understanding Centripetal Acceleration**:
The centripetal acceleration \( A \) of an object moving in a circular path can be expressed in terms of its angular velocity \( \omega \) and the radius \( r \) of the circular path:
\[ A = \omega^2 r \]

2. **Applying the Formula to Both Satellites**:
For the first satellite with radius \( r_1 \):
\[ A_1 = \omega^2 r_1 \]
For the second satellite with radius \( r_2 \):
\[ A_2 = \omega^2 r_2 \]

3. **Comparing the Two Accelerations**:
Since we know that \( r_2 > r_1 \) and both satellites have the same angular velocity \( \omega \), we can compare the two expressions:
\[ A_1 = \omega^2 r_1 \quad \text{and} \quad A_2 = \omega^2 r_2 \]

4. **Establishing the Relationship**:
Since \( r_2 > r_1 \), we can conclude:
\[ A_2 = \omega^2 r_2 > \omega^2 r_1 = A_1 \]
Therefore, we have:
\[ A_2 > A_1 \]

5. **Final Conclusion**:
The centripetal acceleration of the satellite with the larger radius \( r_2 \) is greater than that of the satellite with the smaller radius \( r_1 \):
\[ A_2 > A_1 \]