A 50 kg girl wearing heel shoes balances on a single heel. The heel is circular with a diameter 1 cm. The pressure exerted by the heel on the horizontal floor is `(Take g = 10 m s^(-2))`

Options

A. ` 6.4xx10^(4)` Pa
B. ` 6.4xx10^(5)` Pa
C. ` 6.4xx10^(6)` Pa
D. ` 6.4xx10^(7)` Pa

Explanation

To solve the problem of finding the pressure exerted by the heel of a girl wearing heel shoes, we can follow these steps:

### Step 1: Identify the given values
- Mass of the girl (m) = 50 kg
- Diameter of the heel (d) = 1 cm = 0.01 m (convert to meters)
- Acceleration due to gravity (g) = 10 m/s²

### Step 2: Calculate the weight of the girl
The weight (W) can be calculated using the formula:
\[ W = m \cdot g \]
Substituting the values:
\[ W = 50 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 500 \, \text{N} \]

### Step 3: Calculate the radius of the heel
The radius (r) is half of the diameter:
\[ r = \frac{d}{2} = \frac{0.01 \, \text{m}}{2} = 0.005 \, \text{m} \]

### Step 4: Calculate the area of the heel
The area (A) of the circular heel can be calculated using the formula for the area of a circle:
\[ A = \pi r^2 \]
Substituting the radius:
\[ A = \pi (0.005 \, \text{m})^2 = \pi (0.000025 \, \text{m}^2) \approx 0.00007854 \, \text{m}^2 \]

### Step 5: Calculate the pressure
Pressure (P) is defined as force (or weight in this case) per unit area:
\[ P = \frac{W}{A} \]
Substituting the values:
\[ P = \frac{500 \, \text{N}}{0.00007854 \, \text{m}^2} \approx 63736.8 \, \text{Pa} \]

### Step 6: Convert the pressure to appropriate units
To express this in scientific notation:
\[ P \approx 6.37 \times 10^4 \, \text{Pa} \]

### Final Answer:
The pressure exerted by the heel on the horizontal floor is approximately \( 6.37 \times 10^4 \, \text{Pa} \).

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