In an elastic one dimensional collision between two particles the relative veloctiy of approach before collision is

Options

A. greater than the relative velocity of separation after collision
B. less than the relative velocity of separation after collision
C. equal to the relative velocity of separation after collision
D. less than the relative velocity of separation if the incoming particle is heavier than the target particle

Answer

To solve the problem regarding the relative velocity of approach before an elastic one-dimensional collision, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Elastic Collision:**
In an elastic collision, both momentum and kinetic energy are conserved. The coefficient of restitution (e) is defined as the ratio of the relative velocity of separation to the relative velocity of approach.

2. **Define Relative Velocity of Approach:**
The relative velocity of approach before the collision can be expressed as:
\[ v_{approach} = v_1 - v_2 \]
where \(v_1\) is the velocity of the first particle and \(v_2\) is the velocity of the second particle before the collision.

3. **Define Relative Velocity of Separation:**
The relative velocity of separation after the collision can be expressed as:
\[ v_{separation} = v_2' - v_1' \]
where \(v_1'\) and \(v_2'\) are the velocities of the first and second particles after the collision, respectively.

4. **Use the Coefficient of Restitution:**
The coefficient of restitution (e) relates the relative velocities before and after the collision:
\[ e = \frac{v_{separation}}{v_{approach}} \]
For an elastic collision, \(e = 1\).

5. **Substituting the Value of e:**
Since \(e = 1\) for elastic collisions, we can substitute this into the equation:
\[ 1 = \frac{v_{separation}}{v_{approach}} \]
This simplifies to:
\[ v_{separation} = v_{approach} \]

6. **Conclusion:**
Therefore, in an elastic one-dimensional collision, the relative velocity of approach before the collision is equal to the relative velocity of separation after the collision.

### Final Answer:
The relative velocity of approach before the collision is equal to the relative velocity of separation after the collision.