Young's modulus of steel is `1.9xx10^(11) N//m^2` When expressed is CGS units of `dy"nes"// cm^2` it will be equal to `(1N = 10^5dy"ne", 1 m^2 = 10^4 cm^2)`

Options

A. `1.9xx10^(10)`
B. `1.9xx10^(11)`
C. `1.9xx10^(12)`
D. `1.9xx10^(13)`

Explanation

To convert Young's modulus from SI units (N/m²) to CGS units (dyne/cm²), we will follow these steps:

### Step 1: Write down the given value of Young's modulus in SI units.
The Young's modulus of steel is given as:
\[ Y = 1.9 \times 10^{11} \, \text{N/m}^2 \]

### Step 2: Convert Newtons to dynes.
We know that:
\[ 1 \, \text{N} = 10^5 \, \text{dyne} \]
Thus, we can convert the Young's modulus from Newtons to dynes:
\[ Y = 1.9 \times 10^{11} \, \text{N/m}^2 \times 10^5 \, \text{dyne/N} \]

### Step 3: Convert square meters to square centimeters.
We also know that:
\[ 1 \, \text{m}^2 = 10^4 \, \text{cm}^2 \]
Now, we can express the Young's modulus in terms of dyne/cm²:
\[ Y = \frac{1.9 \times 10^{11} \times 10^5 \, \text{dyne}}{1 \, \text{m}^2} \times \frac{1}{10^4 \, \text{cm}^2} \]

### Step 4: Simplify the expression.
Now, we can simplify the expression:
\[ Y = 1.9 \times 10^{11} \times 10^5 \times \frac{1}{10^4} \, \text{dyne/cm}^2 \]
\[ Y = 1.9 \times 10^{11} \times 10^{5-4} \, \text{dyne/cm}^2 \]
\[ Y = 1.9 \times 10^{11} \times 10^{1} \, \text{dyne/cm}^2 \]
\[ Y = 1.9 \times 10^{12} \, \text{dyne/cm}^2 \]

### Final Answer:
Thus, the Young's modulus of steel in CGS units is:
\[ Y = 1.9 \times 10^{12} \, \text{dyne/cm}^2 \]

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