Statement-I : Path of a projectile is a parabola irrespective of its velocity of projection.
Statement-II : Trajectory of a projectile is a parabola when variation of g, (acceleration due to gravity) can be neglected.

Options

A. Statement-I is true, Statement-II is true, Statement-II is correct explanation for Statement-I
B. Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for Statement-I
C. Statement-I is true, Statement-II is false
D. Statement-I is false, Statement-II is true.

Explanation

To analyze the given statements, let's break down the problem step by step:

### Step 1: Understand Statement-I
**Statement-I**: "The path of a projectile is a parabola irrespective of its velocity of projection."

- A projectile's motion consists of two components: horizontal and vertical.
- The path is a parabola only when both components are present (i.e., when the projectile is launched at an angle).
- If a projectile is launched vertically (with no horizontal component), it will not trace a parabolic path; instead, it will move straight up and then straight down.

**Conclusion**: Statement-I is **false**.

### Step 2: Understand Statement-II
**Statement-II**: "The trajectory of a projectile is a parabola when the variation of g (acceleration due to gravity) can be neglected."

- The trajectory of a projectile is indeed a parabola when the acceleration due to gravity (g) is constant.
- If we consider the motion of a projectile near the Earth's surface, g can be assumed constant for small heights. In this case, the projectile's motion can be modeled as a parabolic trajectory.
- If g varies significantly (e.g., at very high altitudes), the trajectory may not be a perfect parabola.

**Conclusion**: Statement-II is **true**.

### Final Conclusion
- Statement-I is **false**.
- Statement-II is **true**.
- Since Statement-II provides a correct explanation for the conditions under which Statement-I might be true, we conclude that Statement-I is false and Statement-II is true.

### Summary
- **Statement-I**: False
- **Statement-II**: True