The same force F acts on four different objects having the areas given below, one by one. In which case the pressure exerted will be the maximum ?

Options

A. 20 `m^(2)`
B. 50 `m^(2)`
C. 10 `m^(2)`
D. 100 `m^(2)`

Answer

To determine in which case the pressure exerted will be maximum when the same force \( F \) acts on four different objects with varying areas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Pressure Formula**:
The formula for pressure \( P \) is given by:
\[ P = \frac{F}{A} \]
where \( F \) is the force applied, and \( A \) is the area over which the force is applied.

2. **Identify the Areas**:
We have four different areas for the objects:
- Option 1: \( A_1 = 20 \, m^2 \)
- Option 2: \( A_2 = 50 \, m^2 \)
- Option 3: \( A_3 = 10 \, m^2 \)
- Option 4: \( A_4 = 100 \, m^2 \)

3. **Analyze the Relationship Between Area and Pressure**:
From the formula, we can see that pressure is inversely proportional to the area. This means that as the area increases, the pressure decreases. Therefore, to maximize pressure, we need to minimize the area.

4. **Compare the Areas**:
Now, we compare the given areas:
- \( A_1 = 20 \, m^2 \)
- \( A_2 = 50 \, m^2 \)
- \( A_3 = 10 \, m^2 \) (minimum area)
- \( A_4 = 100 \, m^2 \)

5. **Determine the Minimum Area**:
The minimum area among the options is \( A_3 = 10 \, m^2 \).

6. **Conclusion**:
Since pressure is maximum when the area is minimum, the maximum pressure will occur when the force \( F \) is applied to the object with area \( A_3 \). Therefore, the answer is:
\[ \text{The pressure will be maximum in Option 3 with area } 10 \, m^2. \]