If a force of 250 N acts on a body, the momentum acquired is 125 Km m/s, what is the period for which force acts on the body ?

Options

A. 0.2 sec
B. 0.5 sec
C. 0.4 sec
D. 0.25 sec

Explanation

To solve the problem, we need to find the time period for which a force acts on a body given the force and the momentum acquired by the body.

### Step-by-Step Solution:

1. **Understand the Given Data:**
- Force (F) = 250 N
- Momentum acquired (Δp) = 125 kg·m/s

2. **Use the Relationship Between Force, Change in Momentum, and Time:**
According to Newton's second law, the force acting on an object is equal to the rate of change of momentum:
\[ F = \frac{\Delta p}{\Delta t} \]
where:
- \( F \) is the force,
- \( \Delta p \) is the change in momentum,
- \( \Delta t \) is the change in time.

3. **Rearranging the Formula:**
We can rearrange the formula to solve for the time period (Δt):
\[ \Delta t = \frac{\Delta p}{F} \]

4. **Substituting the Known Values:**
Now, substitute the values of Δp and F into the equation:
\[ \Delta t = \frac{125 \, \text{kg·m/s}}{250 \, \text{N}} \]

5. **Calculating the Time Period:**
Perform the division:
\[ \Delta t = \frac{125}{250} = 0.5 \, \text{s} \]

6. **Final Answer:**
The time period for which the force acts on the body is:
\[ \Delta t = 0.5 \, \text{s} \]

### Summary:
The force of 250 N acts on the body for a period of 0.5 seconds to acquire a momentum of 125 kg·m/s.

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