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 \( a_1 \) and \( a_2 \), and their respective radii as \( r_1 \) and \( r_2 \).

### Step-by-Step Solution:

1. **Understand the Formula for Centripetal Acceleration**:
The centripetal acceleration \( a \) of an object moving in a circular path is given by the formula:
\[ a = r \omega^2 \]
where \( r \) is the radius of the circular path and \( \omega \) is the angular velocity.

2. **Write the Expressions for Both Satellites**:
For the first satellite with radius \( r_1 \):
\[ a_1 = r_1 \omega^2 \]
For the second satellite with radius \( r_2 \):
\[ a_2 = r_2 \omega^2 \]

3. **Compare the Centripetal Accelerations**:
Since both satellites have the same angular velocity \( \omega \), we can relate their centripetal accelerations directly through their radii:
\[ \frac{a_1}{a_2} = \frac{r_1 \omega^2}{r_2 \omega^2} = \frac{r_1}{r_2} \]

4. **Substituting the Given Condition**:
We know from the problem statement that \( r_1 < r_2 \). Therefore, it follows that:
\[ \frac{a_1}{a_2} < 1 \quad \text{or} \quad a_1 < a_2 \]

5. **Conclusion**:
The centripetal accelerations of the two satellites are related such that:
\[ a_1 < a_2 \]

### Final Answer:
Thus, the centripetal accelerations of the satellites are related as \( a_1 < a_2 \).

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