A lead ball and rubber ball having same mass, strike normally on a smooth vertical wall with the same velocity. The lead ball falls down after striking but the rubber ball bounces back. Then

Options

A. momentum of lead ball is greater than that of rubber ball
B. momentum of rubber ball is greater than that of lead ball
C. the rubber ball suffers a greater change in momentum as compared to lead ball
D. both the balls suffer an equal change in momentum

Explanation

To solve the problem, we need to analyze the situation of both the lead ball and the rubber ball striking a smooth vertical wall with the same mass and velocity. We will look at their behavior after the collision and calculate their momentum changes.

### Step-by-Step Solution:

1. **Identify the Initial Conditions:**
- Both balls (lead and rubber) have the same mass, denoted as \( m \).
- Both balls strike the wall with the same initial velocity, denoted as \( v \).

2. **Calculate Initial Momentum:**
- The initial momentum of both balls can be calculated using the formula:
\[ \text{Initial Momentum} = \text{mass} \times \text{velocity} \]
- For both balls:
\[ \text{Initial Momentum of Lead Ball} = mv \]
\[ \text{Initial Momentum of Rubber Ball} = mv \]

3. **Analyze the Lead Ball's Collision:**
- Upon striking the wall, the lead ball does not bounce back; it falls down.
- Therefore, its final velocity after the collision is \( 0 \) (it stops moving horizontally).
- The final momentum of the lead ball is:
\[ \text{Final Momentum of Lead Ball} = m \times 0 = 0 \]

4. **Analyze the Rubber Ball's Collision:**
- The rubber ball bounces back after striking the wall.
- If it bounces back with the same speed but in the opposite direction, its final velocity is \( -v \).
- The final momentum of the rubber ball is:
\[ \text{Final Momentum of Rubber Ball} = m \times (-v) = -mv \]

5. **Calculate the Change in Momentum:**
- The change in momentum for the lead ball is:
\[ \Delta p_{\text{Lead}} = \text{Final Momentum} - \text{Initial Momentum} = 0 - mv = -mv \]
- The change in momentum for the rubber ball is:
\[ \Delta p_{\text{Rubber}} = \text{Final Momentum} - \text{Initial Momentum} = -mv - mv = -2mv \]

6. **Conclusion:**
- The lead ball experiences a change in momentum of \( -mv \).
- The rubber ball experiences a change in momentum of \( -2mv \).
- Therefore, the rubber ball suffers a greater change in momentum compared to the lead ball.

### Final Answer:
The rubber ball suffers a greater change in momentum as compared to the lead ball.