STATEMENT-1 : Assuming sun to be a body of very large mass in comparison to all other planets, the angular momentum of all the planets about the sun remains conserved.
because
STATEMENT-2 : Gravitational force is always conservative.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True , Statement-2 is False
D. Statement-1 is False , Statement-2 is True

Answer

To solve the question, we need to analyze both statements and determine their validity and relationship.

### Step 1: Analyze Statement 1
Statement 1 claims that the angular momentum of all the planets about the Sun remains conserved, assuming the Sun has a very large mass compared to the planets.

**Explanation**:
- Angular momentum (L) of a system is given by the product of the moment of inertia (I) and the angular velocity (ω). For planets orbiting the Sun, we can express angular momentum as \( L = mvr \), where \( m \) is the mass of the planet, \( v \) is its tangential velocity, and \( r \) is the distance from the Sun.
- Since the Sun's mass is significantly larger than that of the planets, the gravitational force exerted by the Sun provides a central force that keeps the planets in their orbits.
- According to Kepler's second law, the line connecting a planet to the Sun sweeps out equal areas in equal times, which implies that the areal velocity is constant. This means that the angular momentum of the planets about the Sun is conserved.

**Conclusion**: Statement 1 is true.

### Step 2: Analyze Statement 2
Statement 2 states that the gravitational force is always conservative.

**Explanation**:
- A conservative force is one where the work done by the force on an object moving between two points is independent of the path taken.
- The gravitational force is a central force, meaning it acts along the line joining the centers of two bodies and its magnitude is inversely proportional to the square of the distance between them (Newton's law of gravitation).
- Since gravitational force meets the criteria of a conservative force, it can be concluded that Statement 2 is also true.

**Conclusion**: Statement 2 is true.

### Step 3: Determine the Relationship Between the Statements
While both statements are true, we need to determine if Statement 2 correctly explains Statement 1.

**Explanation**:
- Statement 1 discusses the conservation of angular momentum due to the gravitational force acting as a central force.
- Statement 2, while true, does not specifically explain why the angular momentum of the planets is conserved in the context of their motion around the Sun. The conservation of angular momentum is a consequence of the central nature of the gravitational force, but the statement about gravitational force being conservative does not directly address the conservation of angular momentum.

**Conclusion**: Statement 2 is not a correct explanation for Statement 1.

### Final Conclusion
- Statement 1 is true.
- Statement 2 is true but does not explain Statement 1.
- Therefore, the correct option is that Statement 1 is true, Statement 2 is true, but Statement 2 is not a correct explanation for Statement 1.