For a perfectly elastic collision and a perfectly inelastic collision, values of coefficient of restitution are respectively

Options

A. `0,0`
B. `0,1`
C. `1,1`
D. `1,0`

Answer

To solve the question regarding the values of the coefficient of restitution for perfectly elastic and perfectly inelastic collisions, we can follow these steps:

### Step 1: Understand the Coefficient of Restitution
The coefficient of restitution (e) is defined as the ratio of the relative velocity of separation to the relative velocity of approach between two colliding bodies. It is given by the formula:

\[ e = \frac{\text{Velocity of separation}}{\text{Velocity of approach}} \]

### Step 2: Analyze Perfectly Elastic Collision
In a perfectly elastic collision, both momentum and kinetic energy are conserved. After the collision, the two bodies separate with a certain velocity. The coefficient of restitution for a perfectly elastic collision is:

\[ e = 1 \]

This means that the relative speed after the collision is equal to the relative speed before the collision.

### Step 3: Analyze Perfectly Inelastic Collision
In a perfectly inelastic collision, the two bodies stick together after colliding, and kinetic energy is not conserved (some energy is lost). The coefficient of restitution for a perfectly inelastic collision is:

\[ e = 0 \]

This indicates that there is no relative velocity of separation after the collision; the bodies move together as one mass.

### Step 4: Conclusion
Thus, the values of the coefficient of restitution for perfectly elastic and perfectly inelastic collisions are:

- For perfectly elastic collision: \( e = 1 \)
- For perfectly inelastic collision: \( e = 0 \)

### Final Answer
The values of the coefficient of restitution are:
- Perfectly elastic collision: \( e = 1 \)
- Perfectly inelastic collision: \( e = 0 \)

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