The numerical value of Young's modulus in S.I. unit is `beta`. what is its numerical value in CGS system?

Options

A. `beta`
B. `10beta`
C. `beta//10`
D. `100beta`

Explanation

To find the numerical value of Young's modulus in the CGS system when its value in the SI system is given as `beta`, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Young's Modulus**:
Young's modulus (Y) is defined as the ratio of stress to strain. The formula for Young's modulus is:
\[ Y = \frac{\text{Stress}}{\text{Strain}} \]
Stress is defined as force per unit area.

2. **Units in SI System**:
In the SI system, the unit of force is Newton (N) and the unit of area is square meters (m²). Therefore, the unit of Young's modulus in SI is:
\[ \text{SI unit of } Y = \frac{\text{N}}{\text{m}^2} \]

3. **Convert SI Units to CGS Units**:
We need to convert the units from SI to CGS. In the CGS system:
- 1 Newton (N) = \(10^5\) Dynes (dyn)
- 1 meter (m) = \(10^2\) centimeters (cm)

4. **Substituting the Units**:
Now, substituting these conversions into the formula for Young's modulus:
\[ Y = \frac{10^5 \text{ dyn}}{(10^2 \text{ cm})^2} \]
Simplifying the denominator:
\[ (10^2 \text{ cm})^2 = 10^4 \text{ cm}^2 \]
Thus, we have:
\[ Y = \frac{10^5 \text{ dyn}}{10^4 \text{ cm}^2} \]

5. **Calculating the Numerical Value**:
Simplifying the expression:
\[ Y = 10^{5-4} \text{ dyn/cm}^2 = 10^{1} \text{ dyn/cm}^2 = 10 \text{ dyn/cm}^2 \]

6. **Relating to Beta**:
Since we know that the numerical value of Young's modulus in SI units is `beta`, we can express the value in the CGS system as:
\[ \text{Numerical value in CGS} = 10 \beta \]

### Final Answer:
The numerical value of Young's modulus in the CGS system is \(10 \beta\).