STATEMENT-l : In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
STATEMENT-2 : In an elastic collision, the linear momentum of the system is conserved.

Options

A. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false but the Reason is true.

Explanation

To analyze the given statements regarding elastic collisions, we can break down the solution into a step-by-step format.

### Step 1: Understanding Statement 1
**Statement 1**: In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.

**Analysis**:
In an elastic collision, the principle states that the relative speed of approach before the collision is equal to the relative speed of separation after the collision. This means that if we denote the velocities of two bodies before the collision as \(v_1\) and \(v_2\), and after the collision as \(u_1\) and \(u_2\), the condition can be expressed as:
\[ |v_1 - v_2| = |u_2 - u_1| \]
However, the statement claims that the relative speed after the collision is equal to the relative speed before the collision, which is not necessarily true in terms of their absolute values.

### Step 2: Example Calculation
Let’s consider an example where:
- Body A has a velocity of \(4 \, \text{m/s}\) before the collision.
- Body B has a velocity of \(2 \, \text{m/s}\) before the collision.

Calculating the relative speed before the collision:
\[ \text{Relative speed before} = v_1 - v_2 = 4 \, \text{m/s} - 2 \, \text{m/s} = 2 \, \text{m/s} \]

Now, after the collision, let’s assume:
- Body A has a velocity of \(1 \, \text{m/s}\).
- Body B has a velocity of \(5 \, \text{m/s}\).

Calculating the relative speed after the collision:
\[ \text{Relative speed after} = u_2 - u_1 = 5 \, \text{m/s} - 1 \, \text{m/s} = 4 \, \text{m/s} \]

Since the relative speeds before and after the collision are not equal, **Statement 1 is false**.

### Step 3: Understanding Statement 2
**Statement 2**: In an elastic collision, the linear momentum of the system is conserved.

**Analysis**:
In any collision, if there are no external forces acting on the system, the total linear momentum before the collision is equal to the total linear momentum after the collision. This is a fundamental principle of physics and holds true for elastic collisions as well.

### Step 4: Conclusion
Since we have established that:
- **Statement 1 is false** (the relative speeds are not equal).
- **Statement 2 is true** (momentum is conserved).

The correct answer is that **Assertion is false and Reason is true**.

### Final Answer
The correct option is **4**: Assertion is false and Reason is true.

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