The young's modulus of a material of wire is `12.6 xx 10^(11) "dyne"//cm^(2)`. Its value is `SI` system is

Options

A. `12.6xx10^(12) N//m^(2)`
B. `12.6xx10^(10) N//m^(2)`
C. `12.6xx10^(6) N//m^(2)`
D. `12.6xx10^(8) N//m^(2)`

Explanation

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

### Step 1: Understand the given value
The Young's modulus is given as:
\[ Y = 12.6 \times 10^{11} \text{ dyne/cm}^2 \]

### Step 2: Use the conversion factor
We know that:
\[ 1 \text{ dyne/cm}^2 = 0.1 \text{ N/m}^2 \]
This means that to convert dyne/cm² to N/m², we can multiply by 0.1.

### Step 3: Apply the conversion
Using the conversion factor, we can convert the Young's modulus:
\[ Y = 12.6 \times 10^{11} \text{ dyne/cm}^2 \times 0.1 \text{ N/m}^2 \]

### Step 4: Simplify the expression
Now, we can simplify the expression:
\[ Y = 12.6 \times 10^{11} \times 0.1 \text{ N/m}^2 \]
\[ Y = 12.6 \times 10^{10} \text{ N/m}^2 \]

### Step 5: Final result
Thus, the value of Young's modulus in SI units is:
\[ Y = 12.6 \times 10^{10} \text{ N/m}^2 \]