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 problem, we need to analyze both statements and their implications regarding angular momentum and gravitational forces.

### Step-by-Step Solution:

**Step 1: Understanding Statement 1**
- The statement asserts that the angular momentum of all planets about the sun remains conserved, assuming the sun has a very large mass compared to the planets.
- Angular momentum (\(L\)) for a planet in orbit around the sun can be expressed as:
\[ L = mvr \]
where \(m\) is the mass of the planet, \(v\) is its tangential velocity, and \(r\) is the distance from the sun.

**Hint for Step 1:** Recall the definition of angular momentum and how it relates to mass, velocity, and radius.

**Step 2: Applying Kepler's Laws**
- According to Kepler's laws, particularly the second law, a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time. This implies that the planet's speed varies depending on its distance from the sun.
- When a planet is closer to the sun, it moves faster, and when it is farther away, it moves slower. This variation in speed maintains the conservation of angular momentum.

**Hint for Step 2:** Think about how the area swept out by the planet relates to its velocity and distance from the sun.

**Step 3: Understanding Statement 2**
- Statement 2 claims that the gravitational force is always conservative. A conservative force is one where the work done in moving an object between two points is independent of the path taken.
- The gravitational force meets this criterion, as the work done by gravity in a closed path is zero.

**Hint for Step 3:** Recall the definition of conservative forces and how gravitational force fits into this category.

**Step 4: Analyzing the Relationship Between the Statements**
- While both statements are correct, the second statement does not provide a direct explanation for the first statement.
- The conservation of angular momentum in the context of gravitational forces is due to the absence of external torques acting on the system, which is a consequence of the gravitational force being central and conservative.

**Hint for Step 4:** Consider whether the explanation provided by Statement 2 directly supports the conclusion of Statement 1.

**Step 5: Conclusion**
- Both statements are true:
- Statement 1 is true because the angular momentum of planets about the sun is conserved due to the nature of their orbits and the large mass of the sun.
- Statement 2 is true because gravitational force is a conservative force.
- However, Statement 2 does not explain Statement 1 directly.

### Final Answer:
Both statements are true, but Statement 2 is not the correct explanation for Statement 1.