Statement I: No external force acts on a system of two spheres which undergo a perfectly elastic head-on collision. The minimum kinetic energy of this system is zero if the net momentum of the system is zero.
Statement II: If any two bodies undergo a perfectly elastic head-on collision, at the instant of maximum deformation. the complete kinetic energy of the system is converted to' deformation potential energy of the system.

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 analyze the statements provided in the question, we will break down each statement and evaluate their correctness step by step.

### Step 1: Understanding Statement I
**Statement I:** No external force acts on a system of two spheres which undergo a perfectly elastic head-on collision. The minimum kinetic energy of this system is zero if the net momentum of the system is zero.

1. **Concept of Elastic Collision:** In a perfectly elastic collision, both momentum and kinetic energy are conserved.
2. **Net Momentum Zero:** If the net momentum of the system is zero, it implies that the momentum of one sphere is equal in magnitude and opposite in direction to the momentum of the other sphere.
3. **Minimum Kinetic Energy:** The minimum kinetic energy of the system can indeed be zero if the two spheres come to rest after the collision. This situation occurs when they collide head-on and stick together (which is a perfectly inelastic collision scenario). However, in a perfectly elastic collision, they will bounce off each other, and the kinetic energy cannot be zero unless both have zero velocity, which contradicts the condition of momentum being zero.
4. **Conclusion for Statement I:** The statement is incorrect because the minimum kinetic energy cannot be zero in a perfectly elastic collision when the net momentum is zero.

### Step 2: Understanding Statement II
**Statement II:** If any two bodies undergo a perfectly elastic head-on collision, at the instant of maximum deformation, the complete kinetic energy of the system is converted to deformation potential energy of the system.

1. **Maximum Deformation:** Maximum deformation occurs when the two bodies are closest to each other during the collision.
2. **Energy Conversion:** At the instant of maximum deformation, the kinetic energy is not completely converted into potential energy. The bodies will still have some kinetic energy as they will rebound after the collision.
3. **Conclusion for Statement II:** This statement is incorrect because, at maximum deformation, not all kinetic energy is converted into deformation potential energy; some kinetic energy remains as the bodies will continue to move after the collision.

### Final Conclusion
Both statements are incorrect based on the analysis above.

### Summary of the Solution:
- **Statement I:** Incorrect (minimum kinetic energy is not zero in a perfectly elastic collision with zero net momentum).
- **Statement II:** Incorrect (not all kinetic energy is converted to deformation potential energy at maximum deformation).