The figure represents the momentum time `(p-t)` curve for a particle moving along an axis under the influence of the force.Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively? If `(t_(3)-t_(2))t_(1)`

Options

A. `c` and `b`
B. `a` and `b`
C. `b` and `c`
D. `c` and `a`

Answer

To solve the problem, we need to analyze the momentum-time (p-t) curve and determine the regions where the force acting on the particle is at its maximum and minimum. The relationship between force and momentum is given by Newton's second law, which states that force is equal to the rate of change of momentum with respect to time.

### Step-by-Step Solution:

1. **Understanding the p-t Curve**:
- The momentum-time curve shows how the momentum of the particle changes over time. The slope of this curve at any point gives the force acting on the particle at that moment.

2. **Identifying the Slope**:
- According to Newton's second law, the force \( F \) can be expressed as:
\[ F = \frac{dp}{dt} \]
- This means that the force is equal to the slope of the momentum-time curve.

3. **Finding Maximum and Minimum Force**:
- To find where the force is maximum, we need to look for the region on the curve where the slope is the steepest (i.e., the greatest positive value).
- Conversely, to find where the force is minimum, we look for the region where the slope is the least steep (i.e., the smallest positive value or the most negative value).

4. **Analyzing Regions**:
- Let's denote three regions on the curve as A, B, and C.
- By visually inspecting the p-t curve:
- If region C has the steepest slope, then the force is maximum in this region.
- If region B has the least slope, then the force is minimum in this region.

5. **Conclusion**:
- Therefore, the magnitude of the force is maximum in region C and minimum in region B.

6. **Final Expression**:
- The answer to the question is:
- Maximum force: Region C
- Minimum force: Region B