If a force `200N` acts on a body, the change in momentum is 100 kg m/s. What is the time for which the force acts on th body?

Options

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

Answer

To solve the problem, we will 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 of that object.

### Step-by-Step Solution:

1. **Identify the given values:**
- Force (F) = 200 N
- Change in momentum (Δp) = 100 kg m/s

2. **Use the formula relating force, change in momentum, and time:**
\[ F = \frac{\Delta p}{\Delta t} \]
Here, \(F\) is the force, \(\Delta p\) is the change in momentum, and \(\Delta t\) is the time duration for which the force acts.

3. **Rearrange the formula to solve for time (\(\Delta t\)):**
\[ \Delta t = \frac{\Delta p}{F} \]

4. **Substitute the known values into the equation:**
\[ \Delta t = \frac{100 \, \text{kg m/s}}{200 \, \text{N}} \]

5. **Calculate the time:**
\[ \Delta t = \frac{100}{200} = 0.5 \, \text{s} \]

6. **Conclusion:**
The time for which the force acts on the body is **0.5 seconds**.