A girl of mass `50` kg is wearing high heel sandals . The heels have a cross section of `1"cm"^(2)` . Also consider an elephant of mass `4000` kg with foot area of each foot `250 "cm"^(2)` .
By how much is the pressure exerted by girl is more than that of elephant ?

Options

A. `200xx10^(4)` pascals
B. `210xx10^(4)` pascals
C. `220xx10^(4)` pascals
D. `230xx10^(4)` pascals

Explanation

To find out how much more pressure is exerted by the girl in high heel sandals compared to the elephant, we will follow these steps:

### Step 1: Calculate the pressure exerted by the girl.
1. **Determine the force exerted by the girl (weight)**:
\[ \text{Force} = \text{mass} \times \text{gravity} = 50 \, \text{kg} \times 10 \, \text{m/s}^2 = 500 \, \text{N} \]

2. **Calculate the total area of the heels**:
- Each heel has a cross-sectional area of \(1 \, \text{cm}^2\).
- Since she has two heels, the total area is:
\[ \text{Total Area} = 2 \times 1 \, \text{cm}^2 = 2 \, \text{cm}^2 \]
- Convert \(2 \, \text{cm}^2\) to \(m^2\):
\[ 2 \, \text{cm}^2 = 2 \times 10^{-4} \, \text{m}^2 \]

3. **Calculate the pressure exerted by the girl**:
\[ P_g = \frac{\text{Force}}{\text{Area}} = \frac{500 \, \text{N}}{2 \times 10^{-4} \, \text{m}^2} = \frac{500}{0.0002} = 2500000 \, \text{Pa} = 2.5 \times 10^6 \, \text{Pa} \]

### Step 2: Calculate the pressure exerted by the elephant.
1. **Determine the force exerted by the elephant (weight)**:
\[ \text{Force} = \text{mass} \times \text{gravity} = 4000 \, \text{kg} \times 10 \, \text{m/s}^2 = 40000 \, \text{N} \]

2. **Calculate the total area of the elephant's feet**:
- Each foot has an area of \(250 \, \text{cm}^2\) and the elephant has 4 feet:
\[ \text{Total Area} = 4 \times 250 \, \text{cm}^2 = 1000 \, \text{cm}^2 \]
- Convert \(1000 \, \text{cm}^2\) to \(m^2\):
\[ 1000 \, \text{cm}^2 = 1000 \times 10^{-4} \, \text{m}^2 = 0.1 \, \text{m}^2 \]

3. **Calculate the pressure exerted by the elephant**:
\[ P_e = \frac{\text{Force}}{\text{Area}} = \frac{40000 \, \text{N}}{0.1 \, \text{m}^2} = 400000 \, \text{Pa} = 4 \times 10^5 \, \text{Pa} \]

### Step 3: Calculate the difference in pressure.
1. **Find the difference in pressure**:
\[ \Delta P = P_g - P_e = (2.5 \times 10^6 \, \text{Pa}) - (4 \times 10^5 \, \text{Pa}) = 2.1 \times 10^6 \, \text{Pa} \]

### Final Answer:
The pressure exerted by the girl is \(2.1 \times 10^6 \, \text{Pa}\) more than that of the elephant.

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