A ball of mass m collides with a wall with speed v and rebounds on the same line with the same speed. If the mass of the wall is taken as infinite, then the work done by the ball on the wall is

Options

A. `mv^2`
B. `1/2mv^2`
C. `2mv`
D. zero

Explanation

To solve the problem of finding the work done by a ball of mass \( m \) that collides with a wall and rebounds with the same speed \( v \), we can follow these steps:

### Step 1: Understand the scenario
The ball collides with a wall and rebounds with the same speed. The mass of the wall is considered infinite, which means it does not move or change its state due to the collision.

### Step 2: Define work done
Work done \( W \) is defined as the change in kinetic energy of the system. Mathematically, it can be expressed as:
\[ W = \Delta KE = KE_{\text{final}} - KE_{\text{initial}} \]

### Step 3: Calculate initial and final kinetic energy
- **Initial Kinetic Energy** (\( KE_{\text{initial}} \)):
\[ KE_{\text{initial}} = \frac{1}{2} mv^2 \]
- **Final Kinetic Energy** (\( KE_{\text{final}} \)):
Since the ball rebounds with the same speed \( v \), its final kinetic energy is:
\[ KE_{\text{final}} = \frac{1}{2} mv^2 \]

### Step 4: Calculate the change in kinetic energy
Now, we can find the change in kinetic energy:
\[ \Delta KE = KE_{\text{final}} - KE_{\text{initial}} = \frac{1}{2} mv^2 - \frac{1}{2} mv^2 = 0 \]

### Step 5: Conclusion about work done
Since the change in kinetic energy is zero, the work done by the ball on the wall is:
\[ W = 0 \]

### Final Answer
The work done by the ball on the wall is \( 0 \).

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