This section contains Assertion and Reason type questions. Each question has 4 choices (1), (2), (3) and (4), out of which only one is correct.
Assertion (A) Smaller the orbit of the planet around the sun, shorter is the time it takes to complete one revolution.
Reason (R) According to Kepler’s third law of planetary motion,square of time period is proportional to cube of mean distance from sun

Options

A. If both Assertion and Reason are true and the Reason Is the correct explanation of the Assertion,
B. If both Assertion and Reason are true but Reason Is not the correct explanation of the Assertion.
C. If Assertion Is correct but Reason Is Incorrect.
D. lf Assertion Is Incorrect but Reason Is correct.

Answer

To solve the assertion and reason question, we will analyze both the assertion (A) and the reason (R) step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states: "Smaller the orbit of the planet around the sun, shorter is the time it takes to complete one revolution."
- This implies that if a planet is in a smaller orbit (closer to the sun), it will take less time to complete one full revolution around the sun.

2. **Understanding the Reason (R)**:
- The reason states: "According to Kepler’s third law of planetary motion, the square of the time period is proportional to the cube of the mean distance from the sun."
- Mathematically, this can be expressed as:
\[ T^2 \propto r^3 \]
where \( T \) is the time period of revolution and \( r \) is the mean distance from the sun.

3. **Applying Kepler’s Third Law**:
- From Kepler’s third law, if the mean distance \( r \) is smaller (i.e., the planet is closer to the sun), then \( r^3 \) will also be smaller.
- Consequently, since \( T^2 \) is proportional to \( r^3 \), a smaller \( r \) leads to a smaller \( T^2 \), which means that \( T \) (the time period) must also be smaller.

4. **Conclusion**:
- Therefore, the assertion is true: smaller orbits result in shorter time periods for revolution.
- The reason is also true and correctly explains the assertion based on Kepler’s third law.

5. **Final Answer**:
- Since both the assertion and reason are true, and the reason correctly explains the assertion, the correct choice is option (1): "Both assertion and reason are true, and reason is the correct explanation of assertion."