A body of mass m collides against a wall with the velocity v and rebounds with the same speed. Its magnitude of change of momentum is

Options

A. 2 m v
B. m v
C. `1/2 m v`
D. `0`

Answer

To find the magnitude of the change in momentum of a body of mass \( m \) that collides with a wall with velocity \( v \) and rebounds with the same speed, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Initial Momentum**:
- The initial momentum of the body before collision can be calculated using the formula:
\[ \text{Initial Momentum} = m \cdot v \]
- Here, we consider the direction towards the wall as positive, so the initial momentum is:
\[ p_{\text{initial}} = mv \]

2. **Identify Final Momentum**:
- After colliding with the wall, the body rebounds with the same speed \( v \) but in the opposite direction. Therefore, the final momentum will be:
\[ \text{Final Momentum} = m \cdot (-v) = -mv \]

3. **Calculate Change in Momentum**:
- The change in momentum (\( \Delta p \)) is given by the difference between the final momentum and the initial momentum:
\[ \Delta p = p_{\text{final}} - p_{\text{initial}} = (-mv) - (mv) \]
- Simplifying this gives:
\[ \Delta p = -mv - mv = -2mv \]

4. **Determine the Magnitude of Change in Momentum**:
- Since we are interested in the magnitude of the change in momentum, we take the absolute value:
\[ |\Delta p| = | -2mv | = 2mv \]

Thus, the magnitude of the change in momentum is \( 2mv \).

### Final Answer:
\[ \text{Magnitude of change in momentum} = 2mv \]

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