Assertion : Angular speed of a planet around the sun increases, when it is closer to the sun.
Reason : Total angular momentum of the system remains constant.

Options

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

Explanation

To solve the problem, we will analyze the assertion and the reason step by step.

### Step 1: Understanding the Assertion
The assertion states that the angular speed of a planet around the sun increases when it is closer to the sun.

**Explanation**:
In an elliptical orbit, a planet moves faster when it is closer to the sun (perihelion) due to gravitational attraction. According to Kepler's laws, particularly the second law (the law of areas), a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time. Therefore, when the planet is closer to the sun, it must move faster to cover the same area in the same time.

### Step 2: Understanding the Reason
The reason provided is that the total angular momentum of the system remains constant.

**Explanation**:
Angular momentum \( L \) of a planet in orbit is given by the product of its moment of inertia \( I \) and angular speed \( \omega \):
\[ L = I \cdot \omega \]
In the absence of external torque, the total angular momentum of the system (planet + sun) remains constant. Since the planet's distance from the sun changes, its moment of inertia changes. When the planet is closer to the sun, its moment of inertia decreases, which results in an increase in angular speed to keep the angular momentum constant.

### Step 3: Conclusion
Both the assertion and the reason are true, and the reason correctly explains the assertion.

### Final Answer
- **Assertion**: True
- **Reason**: True
- **Conclusion**: The reason is the correct explanation of the assertion.