Statement I: If a ball projected up obliquely from the ground breaks up into several fragments in its path, the centre of the system of all fragments moves in the same parabolic path compared to initial one till all fragments are in air.
Statement II: In the situation of Statement 1, at the instant of breaking, the fragments may be thrown in different directions with different speeds.

Options

A. Both assertion and reason are true and reason is the correct explanation of assertion.
B. Both assertion and reason are true but reason is not the correct explanation of assertion.
C. Assertion is true and reason is false.
D. Assertion is false and reason is true.

Explanation

To solve the problem, we need to analyze both statements provided and determine their validity based on the principles of the center of mass and projectile motion.

### Step-by-Step Solution:

1. **Understanding Statement I**:
- The statement claims that if a ball projected obliquely breaks into several fragments during its flight, the center of mass of these fragments will continue to move in the same parabolic path as the original ball until all fragments are in the air.
- This is based on the principle of conservation of momentum. When the ball breaks, the total momentum of the system (the ball and its fragments) must be conserved. The center of mass continues to follow the same trajectory because external forces (like gravity) act uniformly on the system.

2. **Analyzing Statement II**:
- The second statement suggests that at the moment of breaking, the fragments can be thrown in different directions with different speeds.
- This is also true. When the ball breaks apart, the fragments can indeed have different velocities and directions due to the forces acting on them at that instant. However, this does not affect the trajectory of the center of mass.

3. **Conclusion**:
- Both statements are true. However, Statement II does not correctly explain Statement I. While the fragments may move in various directions, the center of mass still follows the original parabolic path due to the conservation of momentum.
- Therefore, the correct answer is that both statements are true, but Statement II is not a correct explanation of Statement I.

### Final Answer:
- **Statement I**: True
- **Statement II**: True, but not a correct explanation of Statement I.