If the value of atmospheric pressure is `10^(6)` dyne `cm^(-2)`. Its value in SI units is:

Options

A. `10^(4)` N `m^(-2)`
B. `10^(6)`N `m^(-2)`
C. `10^(5)` N `m^(-2)`
D. `10^(3)` N `m^(-2)`

Explanation

To convert the atmospheric pressure from dyne/cm² to SI units (N/m²), follow these steps:

### Step 1: Understand the given value
The atmospheric pressure is given as \( 10^6 \) dyne/cm².

### Step 2: Convert dyne to newton
We know that:
- \( 1 \text{ Newton} = 10^5 \text{ dyne} \)

Thus, to convert dyne to newton, we can use the relation:
- \( 1 \text{ dyne} = 10^{-5} \text{ Newton} \)

### Step 3: Convert cm² to m²
We also know that:
- \( 1 \text{ meter} = 100 \text{ centimeters} \)
- Therefore, \( 1 \text{ cm} = 10^{-2} \text{ m} \)

Thus, for area:
- \( 1 \text{ cm}^2 = (10^{-2} \text{ m})^2 = 10^{-4} \text{ m}^2 \)

### Step 4: Substitute the conversions into the pressure equation
Now, we can substitute these conversions into the atmospheric pressure equation:
\[ \text{Pressure} = 10^6 \text{ dyne/cm}^2 = 10^6 \times (10^{-5} \text{ N})/(10^{-4} \text{ m}^2) \]

### Step 5: Simplify the expression
This simplifies to:
\[ = 10^6 \times 10^{-5} \text{ N} \times 10^4 \text{ m}^{-2} \]
\[ = 10^{6 - 5 + 4} \text{ N/m}^2 \]
\[ = 10^{5} \text{ N/m}^2 \]

### Step 6: Conclusion
Thus, the value of atmospheric pressure in SI units is:
\[ 10^{5} \text{ N/m}^2 \]

### Final Answer
The correct option is \( 10^{5} \text{ N/m}^2 \).

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