The two femurs each of cross-sectional area `10 cm^(2)` support the upper part of a human body of mass 40 kg. the average pressure sustained by the femurs is (take `g=10 ms^(-2))`

Options

A. `2 xx 10^(2) N m^(-2)`
B. `2 xx 10^(4) N m^(-2)`
C. `2 xx 10^(5) N m^(-2)`
D. `2 xx 10^(6) N m^(-2)`

Explanation

To find the average pressure sustained by the femurs, we can follow these steps:

### Step 1: Identify the given values
- Mass of the upper body (m) = 40 kg
- Acceleration due to gravity (g) = 10 m/s²
- Cross-sectional area of one femur (A) = 10 cm²

### Step 2: Convert the cross-sectional area to SI units
Since the area is given in cm², we need to convert it to m²:
\[ 1 \text{ cm}^2 = 10^{-4} \text{ m}^2 \]
Thus,
\[ A = 10 \text{ cm}^2 = 10 \times 10^{-4} \text{ m}^2 = 10^{-3} \text{ m}^2 \]

### Step 3: Calculate the total cross-sectional area of both femurs
Since there are two femurs, the total area (A_total) is:
\[ A_{\text{total}} = 2 \times A = 2 \times 10^{-3} \text{ m}^2 = 2 \times 10^{-3} \text{ m}^2 \]

### Step 4: Calculate the force exerted by the body
The force (F) exerted by the body is equal to its weight, which can be calculated using the formula:
\[ F = m \cdot g \]
Substituting the values:
\[ F = 40 \text{ kg} \times 10 \text{ m/s}^2 = 400 \text{ N} \]

### Step 5: Calculate the average pressure sustained by the femurs
Pressure (P) is defined as force per unit area:
\[ P = \frac{F}{A_{\text{total}}} \]
Substituting the values we calculated:
\[ P = \frac{400 \text{ N}}{2 \times 10^{-3} \text{ m}^2} = \frac{400}{0.002} = 200000 \text{ N/m}^2 \]
This can also be expressed in Pascals (Pa):
\[ P = 2 \times 10^5 \text{ Pa} \]

### Final Answer
The average pressure sustained by the femurs is:
\[ P = 2 \times 10^5 \text{ Pa} \]

---