A body of mass 5kg undergoes a change in speed from 20 to 0.20 m/s. The momentum of the body would

Options

A. increase by 99kgm/s
B. decrease by 99kgm/s
C. increase by 101kgm/s
D. decrease by 101 kgm/s

Answer

To solve the problem of how the momentum of a body changes as its speed decreases from 20 m/s to 0.20 m/s, we will follow these steps:

### Step 1: Understand the concept of momentum
Momentum (P) is defined as the product of mass (m) and velocity (v). The formula for momentum is:
\[ P = m \times v \]

### Step 2: Identify the given values
- Mass of the body, \( m = 5 \, \text{kg} \)
- Initial velocity, \( v_1 = 20 \, \text{m/s} \)
- Final velocity, \( v_2 = 0.20 \, \text{m/s} \)

### Step 3: Calculate the initial momentum (P1)
Using the formula for momentum:
\[ P_1 = m \times v_1 \]
Substituting the values:
\[ P_1 = 5 \, \text{kg} \times 20 \, \text{m/s} = 100 \, \text{kg m/s} \]

### Step 4: Calculate the final momentum (P2)
Now, we calculate the final momentum using the final velocity:
\[ P_2 = m \times v_2 \]
Substituting the values:
\[ P_2 = 5 \, \text{kg} \times 0.20 \, \text{m/s} = 1 \, \text{kg m/s} \]

### Step 5: Determine the change in momentum
To find the change in momentum, we subtract the final momentum from the initial momentum:
\[ \text{Change in momentum} = P_1 - P_2 \]
Substituting the values:
\[ \text{Change in momentum} = 100 \, \text{kg m/s} - 1 \, \text{kg m/s} = 99 \, \text{kg m/s} \]

### Step 6: Conclusion
Since the momentum has decreased, the final answer is that the momentum of the body decreased by 99 kg m/s.

### Final Answer
The momentum of the body would decrease by 99 kg m/s.

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