The pressure due to a man weighing `80` kg standing on his feet is `x xx10^(4)"N m"^(-2)` . Area of his feet is `160 "cm"^(2)` . Find the value of `x.(g=10"ms"^(-2))` .

Explanation

To solve the problem step by step, we will calculate the pressure exerted by the man standing on his feet.

### Step 1: Calculate the weight of the man
The weight \( W \) of the man can be calculated using the formula:
\[ W = m \cdot g \]
where:
- \( m = 80 \, \text{kg} \) (mass of the man)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Substituting the values:
\[ W = 80 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 800 \, \text{N} \]

### Step 2: Convert the area from cm² to m²
The area \( A \) of the man's feet is given as:
\[ A = 160 \, \text{cm}^2 \]
To convert this to square meters, we use the conversion factor \( 1 \, \text{cm}^2 = 10^{-4} \, \text{m}^2 \):
\[ A = 160 \, \text{cm}^2 \cdot 10^{-4} \, \text{m}^2/\text{cm}^2 = 160 \times 10^{-4} \, \text{m}^2 = 1.6 \times 10^{-2} \, \text{m}^2 \]

### Step 3: Calculate the pressure
Pressure \( P \) is defined as the force per unit area:
\[ P = \frac{F}{A} \]
Substituting the values we have:
\[ P = \frac{800 \, \text{N}}{1.6 \times 10^{-2} \, \text{m}^2} \]

### Step 4: Simplify the pressure calculation
Calculating the pressure:
\[ P = \frac{800}{1.6 \times 10^{-2}} = \frac{800}{0.016} = 50000 \, \text{N/m}^2 = 5 \times 10^4 \, \text{N/m}^2 \]

### Step 5: Determine the value of \( x \)
From the problem statement, we know that:
\[ P = x \times 10^4 \, \text{N/m}^2 \]
Comparing this with our calculated pressure:
\[ 5 \times 10^4 \, \text{N/m}^2 = x \times 10^4 \, \text{N/m}^2 \]
Thus, we can conclude:
\[ x = 5 \]

### Final Answer
The value of \( x \) is \( 5 \).

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