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 find the initial momentum of the body, we can follow these steps:

### Step 1: Understand the Given Information
We know that:
- A body is moving with uniform velocity (initial velocity \( u \)).
- It is stopped by a retarding force of \( 200 \, \text{N} \) in \( 0.25 \, \text{s} \).
- The final velocity \( v = 0 \).

### Step 2: Apply Newton's Second Law
According to Newton's second law, the force \( F \) is equal to the rate of change of momentum:
\[ F = \frac{dp}{dt} \]
where \( p \) is momentum.

### Step 3: Express Change in Momentum
The change in momentum can be expressed as:
\[ F = \frac{p_f - p_i}{\Delta t} \]
where:
- \( p_f \) is the final momentum,
- \( p_i \) is the initial momentum,
- \( \Delta t \) is the time interval (0.25 s).

### Step 4: Substitute Known Values
We know:
- \( F = -200 \, \text{N} \) (the force is retarding, hence negative),
- \( p_f = 0 \) (since the body is stopped),
- \( \Delta t = 0.25 \, \text{s} \).

Substituting these values into the equation gives:
\[ -200 = \frac{0 - p_i}{0.25} \]

### Step 5: Rearrange the Equation
Rearranging the equation to solve for \( p_i \):
\[ -200 \times 0.25 = -p_i \]
\[ -50 = -p_i \]
\[ p_i = 50 \, \text{kg m/s} \]

### Step 6: Conclusion
The initial momentum of the body is:
\[ \boxed{50 \, \text{kg m/s}} \]

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