A metal ball hits a wall and does not rebound whereas a rubber ball of the same mass on hitting the wall the same velocity rebounds back. It can be concluded that–

Options

A. metal ball suffers greater change in momentum
B. rubber ball suffers greater change in momentum .
C. the initial momentum of metal ball is greater than the initial momentum of rubber ball.
D. both suffer same change in momentum .

Answer

To solve the problem, we need to analyze the collision of the two balls (metal and rubber) with the wall in terms of momentum change.

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- A metal ball hits a wall and does not rebound.
- A rubber ball of the same mass hits the wall and rebounds back.
- Both balls are initially moving towards the wall with the same velocity.

2. **Defining Momentum**:
- Momentum (p) is defined as the product of mass (m) and velocity (v):
\[ p = mv \]

3. **Calculating Initial Momentum**:
- For both balls before hitting the wall, the initial momentum is:
\[ p_{\text{initial}} = mv \quad (\text{for both balls}) \]

4. **Calculating Final Momentum**:
- For the metal ball:
- After hitting the wall, it does not rebound, so its final velocity is 0.
- Therefore, the final momentum of the metal ball is:
\[ p_{\text{final, metal}} = 0 \]
- For the rubber ball:
- After hitting the wall, it rebounds back with the same speed but in the opposite direction.
- If we consider the direction towards the wall as positive, the final momentum of the rubber ball is:
\[ p_{\text{final, rubber}} = -mv \]

5. **Calculating Change in Momentum**:
- Change in momentum is calculated as:
\[ \Delta p = p_{\text{final}} - p_{\text{initial}} \]
- For the metal ball:
\[ \Delta p_{\text{metal}} = 0 - mv = -mv \]
- For the rubber ball:
\[ \Delta p_{\text{rubber}} = -mv - mv = -2mv \]

6. **Comparing Changes in Momentum**:
- The change in momentum for the metal ball is \(-mv\).
- The change in momentum for the rubber ball is \(-2mv\).
- This indicates that the rubber ball experiences a greater change in momentum compared to the metal ball.

7. **Conclusion**:
- From the analysis, we can conclude that the rubber ball suffers a greater change in momentum than the metal ball.

### Final Answer:
The rubber ball suffers a greater change in momentum than the metal ball.