A mass m with velocity u strikes a wall normally and returns with same speed. What is the magnitude of the change in momentum of the body when it returns.

Options

A. 4 mu
B. mu
C. 2mu
D. zero

Explanation

To solve the problem of finding the magnitude of the change in momentum when a mass \( m \) strikes a wall normally and returns with the same speed, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Initial Momentum:**
The initial momentum \( p_i \) of the mass when it is moving towards the wall with velocity \( u \) is given by:
\[ p_i = m \cdot u \]

2. **Identify Final Momentum:**
After striking the wall, the mass returns with the same speed but in the opposite direction. Therefore, the final momentum \( p_f \) is:
\[ p_f = m \cdot (-u) = -m \cdot u \]

3. **Calculate Change in Momentum:**
The change in momentum \( \Delta p \) is calculated as the difference between the final momentum and the initial momentum:
\[ \Delta p = p_f - p_i \]
Substituting the values we found:
\[ \Delta p = (-m \cdot u) - (m \cdot u) \]
\[ \Delta p = -m \cdot u - m \cdot u = -2m \cdot u \]

4. **Determine Magnitude of Change in Momentum:**
The magnitude of the change in momentum is the absolute value of \( \Delta p \):
\[ |\Delta p| = | -2m \cdot u | = 2m \cdot u \]

### Final Answer:
The magnitude of the change in momentum of the body when it returns is:
\[ 2m \cdot u \]