Assertion: The time period of revolution of a satellite close to surface of earth is smaller then that revolving away from surface of earth.
Reason: The square of time period of revolution of a satellite is directely proportioanl to cube of its orbital radius.

Options

A. If both the assertion and reason are true and reason is a true explantion of the assertion.
B. If both the assertion and reason are true but the reason is not true the correct explantion of the assertion.
C. If the assertion is true but reason false
D. If both the assertion and reason are false.

Explanation

To solve the assertion and reason question, we need to analyze both statements and determine their validity based on the principles of gravitation and orbital mechanics.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that the time period of revolution of a satellite close to the surface of the Earth is smaller than that of a satellite revolving away from the surface of the Earth.
- This implies that satellites in lower orbits (closer to Earth) have shorter orbital periods compared to those in higher orbits.

2. **Understanding the Reason**:
- The reason provided states that the square of the time period (T²) of revolution of a satellite is directly proportional to the cube of its orbital radius (r³).
- This relationship can be expressed mathematically as:
\[ T^2 \propto r^3 \]
- According to Kepler's Third Law of Planetary Motion, this relationship holds true for any satellite orbiting a central body.

3. **Applying the Concepts**:
- For a satellite close to the Earth's surface, the orbital radius (r) is approximately equal to the Earth's radius (R) since the height (h) above the surface is negligible.
- For a satellite further away, the orbital radius is greater than R (i.e., \( r = R + h \) where h is significant).
- Since \( T^2 \propto r^3 \), if the orbital radius (r) increases, the time period (T) will also increase.

4. **Conclusion**:
- Therefore, the assertion is correct: the time period of a satellite close to the surface of the Earth is indeed smaller than that of a satellite revolving away from the surface.
- The reason is also correct: the square of the time period is directly proportional to the cube of the orbital radius.
- Thus, both the assertion and the reason are true, and the reason correctly explains the assertion.

### Final Answer:
- Both the assertion and the reason are true, and the reason correctly explains the assertion.