Assertion : The time period of a satellite revolving very close to the surface of earth is less.
Reason : According to Kepler's law, square of time period of revolution is directly proportional to the cube of semi-major axis.

Options

A. If both assertion and reason are correct and reason is a correct explanation of the assertion.
B. If both assertion and reason are correct but reason is not the correct explanation of assertion.
C. If assertion is correct but reason is incorrect.
D. If assertion is incorrect but reason is correct.

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that "the time period of a satellite revolving very close to the surface of the Earth is less."

- A satellite that is closer to the Earth experiences a stronger gravitational pull, which causes it to move faster in its orbit. Therefore, the time period (T) of the satellite, which is the time it takes to complete one full orbit, will be shorter for satellites that are closer to the Earth.

### Step 2: Understand the Reason
The reason given is based on Kepler's law, which states that "the square of the time period of revolution is directly proportional to the cube of the semi-major axis."

- Mathematically, this can be expressed as:
\[ T^2 \propto R^3 \]
where \( T \) is the time period and \( R \) is the semi-major axis of the orbit. For a satellite in a circular orbit close to the Earth, the semi-major axis is approximately equal to the radius of the Earth plus the altitude of the satellite.

### Step 3: Apply Kepler's Law
If we consider two satellites, one closer to the Earth (let's call it Satellite 1) and one farther away (Satellite 2), we can denote their semi-major axes as \( R_1 \) and \( R_2 \) respectively, where \( R_1 < R_2 \).

- According to Kepler's law:
\[ T_1^2 \propto R_1^3 \]
\[ T_2^2 \propto R_2^3 \]

Since \( R_1 < R_2 \), it follows that:
- \( R_1^3 < R_2^3 \)
- Therefore, \( T_1^2 < T_2^2 \), which implies \( T_1 < T_2 \).

### Step 4: Conclusion
From the above analysis, we conclude that:
- The assertion is correct: The time period of a satellite close to the Earth's surface is indeed less than that of a satellite further away.
- The reason is also correct and accurately explains the assertion according to Kepler's law.

Thus, both the assertion and reason are correct, and the reason provides a correct explanation for the assertion.

### Final Answer
Both the assertion and reason are correct, and the reason is a correct explanation of the assertion.

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