A body moving with uniform velocity is stopped in 0.25 second by applying a retarding force of 200 Newton. The intial momentum of the body will be :-

Options

A. 50 N-s
B. 100 N-s
C. 150 N-s
D. Zero

Answer

To solve the problem of finding the initial momentum of a body that is stopped by a retarding force, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have a body moving with uniform velocity that is stopped by a retarding force of 200 Newtons in 0.25 seconds. We need to find the initial momentum of the body.

2. **Identify the Variables**:
- Retarding Force (F) = 200 N
- Time (Δt) = 0.25 s
- Final momentum (P_final) = 0 (since the body stops)

3. **Use the Momentum Change Formula**: The change in momentum (ΔP) can be calculated using the formula:
\[ \Delta P = F \times \Delta t \]

4. **Calculate the Change in Momentum**:
- Substitute the values into the formula:
\[ \Delta P = 200 \, \text{N} \times 0.25 \, \text{s} = 50 \, \text{N·s} \]

5. **Relate Change in Momentum to Initial Momentum**:
- The change in momentum is given by:
\[ \Delta P = P_{final} - P_{initial} \]
- Since \( P_{final} = 0 \):
\[ \Delta P = 0 - P_{initial} = -P_{initial} \]
- Therefore:
\[ -P_{initial} = 50 \, \text{N·s} \]

6. **Solve for Initial Momentum**:
- Rearranging gives:
\[ P_{initial} = -50 \, \text{N·s} \]
- The negative sign indicates the direction of the momentum is opposite to the direction of the applied force.

### Final Answer:
The initial momentum of the body is \( 50 \, \text{N·s} \) (with the understanding that the negative sign indicates direction).

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