Young 's modulus of steel is `2.0 xx 10^(11)N m//(2) `. Express it is `"dyne"/cm^(2)`.

Explanation

To convert Young's modulus from N/m² to dyne/cm², we can follow these steps:

### Step 1: Write down the given value
The Young's modulus of steel is given as:
\[ Y = 2.0 \times 10^{11} \, \text{N/m}^2 \]

### Step 2: Convert Newtons to Dynes
We know that:
\[ 1 \, \text{N} = 10^5 \, \text{dynes} \]
Therefore, we can convert the Young's modulus from N to dynes:
\[ Y = 2.0 \times 10^{11} \, \text{N/m}^2 \times 10^5 \, \text{dynes/N} \]
This gives us:
\[ Y = 2.0 \times 10^{11} \times 10^5 \, \text{dynes/m}^2 \]

### Step 3: Convert m² to cm²
Next, we need to convert the area from m² to cm². We know that:
\[ 1 \, \text{m} = 100 \, \text{cm} \]
Thus,
\[ 1 \, \text{m}^2 = (100 \, \text{cm})^2 = 10^4 \, \text{cm}^2 \]
Now we can substitute this into our equation:
\[ Y = \frac{2.0 \times 10^{11} \times 10^5 \, \text{dynes}}{10^4 \, \text{cm}^2} \]

### Step 4: Simplify the expression
Now we simplify the expression:
\[ Y = \frac{2.0 \times 10^{11} \times 10^5}{10^4} \, \text{dynes/cm}^2 \]
This simplifies to:
\[ Y = 2.0 \times 10^{11 + 5 - 4} \, \text{dynes/cm}^2 \]
\[ Y = 2.0 \times 10^{12} \, \text{dynes/cm}^2 \]

### Final Result
Thus, the Young's modulus of steel expressed in dyne/cm² is:
\[ Y = 2.0 \times 10^{12} \, \text{dyne/cm}^2 \]

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