A pressure of `10^(6)" dyne"//cm^(2)` is equivalent to :

Options

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

Answer

To solve the given problem, we need to convert the pressure from dyne/cm² to N/m² (Pascal).

Given:
\[ \text{Pressure} = 10^6 \, \text{dyne/cm}^2 \]

### Step-by-Step Solution:

1. **Convert dyne to Newtons:**
- We know that \( 1 \, \text{dyne} = 10^{-5} \, \text{N} \).
- Therefore, \( 10^6 \, \text{dyne} = 10^6 \times 10^{-5} \, \text{N} = 10 \, \text{N} \).

2. **Convert cm² to m²:**
- We know that \( 1 \, \text{cm} = 10^{-2} \, \text{m} \).
- Therefore, \( 1 \, \text{cm}^2 = (10^{-2} \, \text{m})^2 = 10^{-4} \, \text{m}^2 \).

3. **Convert dyne/cm² to N/m²:**
- Given pressure in dyne/cm² is \( 10^6 \, \text{dyne/cm}^2 \).
- Using the conversions:
\[ 10^6 \, \text{dyne/cm}^2 = 10 \, \text{N} / 10^{-4} \, \text{m}^2 \]
- Simplifying the above expression:
\[ 10 \, \text{N} / 10^{-4} \, \text{m}^2 = 10 \times 10^4 \, \text{N/m}^2 = 10^5 \, \text{N/m}^2 \]

Thus, the pressure of \( 10^6 \, \text{dyne/cm}^2 \) is equivalent to \( 10^5 \, \text{N/m}^2 \).

### Final Answer:
\[ \boxed{10^5 \, \text{N/m}^2} \]