A ball of mass `m` moves with speed `v` and stricks a wall having infinite mass and it returns with same speed then the work done by the ball on the wall is

Options

A. Zero
B. `mv joules`
C. `m//v joules`
D. `v//m joules`

Explanation

To solve the problem of the work done by a ball of mass `m` that strikes a wall with infinite mass and returns with the same speed, we can follow these steps:

### Step 1: Understand the Initial Conditions
The ball has a mass `m` and is moving with an initial speed `v` towards the wall. The wall is considered to have an infinite mass, meaning it does not move upon impact.

### Step 2: Calculate the Initial Kinetic Energy
The initial kinetic energy (KE_initial) of the ball before it strikes the wall can be calculated using the formula:
\[ KE_{\text{initial}} = \frac{1}{2} m v^2 \]

### Step 3: Analyze the Collision
When the ball strikes the wall, it comes to a momentary stop before reversing direction. The wall does not move because it has infinite mass. Therefore, the final velocity of the ball after the collision is `-v` (it moves in the opposite direction).

### Step 4: Calculate the Final Kinetic Energy
The final kinetic energy (KE_final) of the ball after it rebounds can be calculated as:
\[ KE_{\text{final}} = \frac{1}{2} m (-v)^2 = \frac{1}{2} m v^2 \]

### Step 5: Calculate the Change in Kinetic Energy
The work done by the ball on the wall can be determined by the change in kinetic energy:
\[ \Delta KE = KE_{\text{final}} - KE_{\text{initial}} \]
Substituting the values we calculated:
\[ \Delta KE = \frac{1}{2} m v^2 - \frac{1}{2} m v^2 = 0 \]

### Step 6: Conclusion
The work done by the ball on the wall is zero because the change in kinetic energy is zero. The ball returns to its original speed after the collision, meaning there is no net work done on the wall.

### Final Answer
The work done by the ball on the wall is **0 Joules**.