Statement I. A particle strikes head-on with another stationary particle such that the first particle comes to rest after collision. The collision should necessarily be elastic.
Statement II: In elastic collision, there is no loss of momentum of the system of the particles.

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 question, we need to analyze both statements regarding the collision of two particles.

### Step-by-Step Solution:

1. **Understanding Statement I**:
- The first particle strikes a stationary second particle and comes to rest after the collision.
- For this scenario to occur, the first particle must transfer all its momentum to the second particle.

2. **Momentum Conservation**:
- According to the law of conservation of momentum, the total momentum before the collision must equal the total momentum after the collision.
- If the first particle (mass \( m_1 \)) has an initial velocity \( v \) and the second particle (mass \( m_2 \)) is stationary (initial velocity = 0), then:
\[ m_1 v + m_2 \cdot 0 = m_1 \cdot 0 + m_2 v' \]
- This simplifies to:
\[ m_1 v = m_2 v' \]
- Here, \( v' \) is the velocity of the second particle after the collision.

3. **Condition for Rest**:
- For the first particle to come to rest, it must transfer all its momentum to the second particle. This can only happen if the masses are equal, i.e., \( m_1 = m_2 \).
- If \( m_1 \) is not equal to \( m_2 \), the first particle cannot come to rest while transferring all its momentum.

4. **Understanding Statement II**:
- Statement II claims that in elastic collisions, there is no loss of momentum in the system.
- This statement is true for both elastic and inelastic collisions. The momentum of the system is conserved in both types of collisions, provided there are no external forces acting on the system.

5. **Conclusion**:
- Statement I is false because it only holds true under the condition that the masses of the two particles are equal.
- Statement II is true as momentum is conserved in all types of collisions.

### Final Answer:
- **Statement I**: False
- **Statement II**: True
- Therefore, the correct answer is that Statement I is false and Statement II is true.