Assertion: Two bodies moving in opposite directions with same magnitude of linear momentum collide each other. Then, after collision both the bodies will come to rest.
Reason: Linear momentum of the system of bodies is zero.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the question, we will analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that two bodies moving in opposite directions with the same magnitude of linear momentum collide and then come to rest after the collision.

**Analysis**:
- Let’s denote the two bodies as \( m_1 \) and \( m_2 \).
- If \( m_1 \) is moving in one direction with momentum \( p_1 = m_1 v_1 \) and \( m_2 \) is moving in the opposite direction with momentum \( p_2 = m_2 v_2 \), and if both have the same magnitude of momentum, we can write:
\[ m_1 v_1 = m_2 v_2 \]
- When they collide, for them to come to rest, all their momentum must be transferred or canceled out. However, this is not generally the case in real collisions unless they are perfectly inelastic and have equal mass and speed.

### Step 2: Understand the Reason
The reason states that the linear momentum of the system of bodies is zero.

**Analysis**:
- If the two bodies have equal and opposite momentum, then:
\[ p_{total} = p_1 + (-p_2) = m_1 v_1 - m_2 v_2 = 0 \]
- This means that the total linear momentum of the system is indeed zero before the collision.

### Step 3: Conclusion
- The assertion is **false** because while the momenta are equal and opposite, it does not imply that the bodies will come to rest after the collision.
- The reason is **true** because the total linear momentum of the system is zero.

### Final Answer
The assertion is false, but the reason is true. Therefore, the correct answer is D: Assertion is false, Reason is true.

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