To convert \(1 \, \text{N/m}^2\) into \(\text{dyne/cm}^2\), we can follow these steps:
### Step 1: Understand the relationship between Newtons and dynes
1 Newton (N) is equivalent to \(10^5\) dynes (dyn). This is the first conversion we need.
### Step 2: Understand the relationship between square meters and square centimeters
1 meter (m) is equivalent to 100 centimeters (cm). Therefore, when we square this conversion:
\[
1 \, \text{m}^2 = (100 \, \text{cm})^2 = 10^4 \, \text{cm}^2
\]
### Step 3: Combine the conversions
Now, we can combine the conversions from step 1 and step 2 to convert \(1 \, \text{N/m}^2\) to \(\text{dyne/cm}^2\):
\[
1 \, \text{N/m}^2 = \frac{10^5 \, \text{dyn}}{10^4 \, \text{cm}^2}
\]
### Step 4: Simplify the expression
Now, we simplify the fraction:
\[
1 \, \text{N/m}^2 = \frac{10^5}{10^4} \, \text{dyne/cm}^2 = 10^{5-4} \, \text{dyne/cm}^2 = 10^1 \, \text{dyne/cm}^2 = 10 \, \text{dyne/cm}^2
\]
### Final Answer
Thus, we conclude that:
\[
1 \, \text{N/m}^2 = 10 \, \text{dyne/cm}^2
\]
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