To solve the question, we need to analyze both statements regarding the behavior of two particles during a completely inelastic collision and the principle of conservation of momentum.
### Step 1: Analyze Statement 1
**Statement 1**: "Two particles moving in the same direction do not lose all their energy in a completely inelastic collision."
- In a completely inelastic collision, two objects collide and stick together, moving as a single object after the collision.
- Even though kinetic energy is not conserved in completely inelastic collisions, momentum is conserved.
- When two particles collide and stick together, they will have a final velocity that is a combination of their initial velocities. This means they do not come to a complete stop; thus, they retain some kinetic energy.
- Therefore, Statement 1 is **correct** because the particles do not lose all their energy; they lose some kinetic energy but not all.
### Step 2: Analyze Statement 2
**Statement 2**: "The principle of conservation of momentum holds true for all kinds of collisions."
- The principle of conservation of momentum states that if no external forces act on a system, the total momentum of that system remains constant.
- This principle applies to all types of collisions: elastic, inelastic, and completely inelastic.
- Since there are no external forces acting during the collision of the two particles, momentum is conserved regardless of the type of collision.
- Therefore, Statement 2 is also **correct**.
### Step 3: Determine the Relationship Between the Statements
- Since Statement 1 is correct, we need to check if Statement 2 provides a correct explanation for Statement 1.
- Statement 2 explains that momentum conservation applies to all collisions, which is the reason why the two particles do not lose all their energy in a completely inelastic collision.
- Thus, Statement 2 indeed serves as a correct explanation for Statement 1.
### Conclusion
Both statements are correct, and Statement 2 is a correct explanation for Statement 1. Therefore, the answer to the question is:
**Option 1: Statement 1 is correct, Statement 2 is correct, and Statement 2 is a correct explanation for Statement 1.**
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