A metalic ball strikes a wall and drops dead whereas tennis ball having the same mass and velocity bounces back. Which of the following is correct ?

Options

A. The Tennis ball suffers a greater change in momentum
B. Metalic ball suffers a greater change in momentum
C. The momentum of the tennis ball is graeater than that of metallic ball before collision
D. The momentum of the metallic ball is greater than the tennis ball before collision

Answer

To solve the problem, we need to analyze the behavior of the two balls (the metallic ball and the tennis ball) when they strike the wall and determine the changes in momentum for each.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Both balls (metallic ball and tennis ball) have the same mass (m) and the same initial velocity (v) before striking the wall.

2. **Analyze the Collision of the Tennis Ball**:
- When the tennis ball strikes the wall, it bounces back with the same speed (v) in the opposite direction.
- The initial momentum of the tennis ball before the collision is \( p_i = mv \) (moving towards the wall).
- After the collision, the final momentum of the tennis ball is \( p_f = -mv \) (moving away from the wall).
- The change in momentum (\( \Delta p \)) for the tennis ball can be calculated as:
\[ \Delta p_{tennis} = p_f - p_i = (-mv) - (mv) = -2mv \]
- The magnitude of the change in momentum is \( 2mv \).

3. **Analyze the Collision of the Metallic Ball**:
- When the metallic ball strikes the wall, it does not bounce back; instead, it drops down.
- The initial momentum of the metallic ball before the collision is \( p_i = mv \) (moving towards the wall).
- After the collision, since it drops dead, its final momentum is \( p_f = 0 \) (it has no momentum after it drops).
- The change in momentum (\( \Delta p \)) for the metallic ball can be calculated as:
\[ \Delta p_{metallic} = p_f - p_i = 0 - (mv) = -mv \]
- The magnitude of the change in momentum is \( mv \).

4. **Compare the Changes in Momentum**:
- Change in momentum for the tennis ball: \( 2mv \)
- Change in momentum for the metallic ball: \( mv \)
- Since \( 2mv > mv \), the tennis ball experiences a greater change in momentum than the metallic ball.

5. **Conclusion**:
- Therefore, the correct statement is that the tennis ball suffers a greater change in momentum compared to the metallic ball.

### Final Answer:
The correct option is that the tennis ball suffers a greater change in momentum.

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