The dimensional formula for young's modulus is

Options

A. `ML^(-1)T^(2)`
B. `M^(0)LT^(-2)`
C. `MLT^(-2)`
D. `ML^(2)T^(-2)`

Answer

To find the dimensional formula for Young's modulus, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Young's Modulus**:
Young's modulus (Y) is defined as the ratio of stress to strain. Mathematically, it can be expressed as:
\[ Y = \frac{\text{Stress}}{\text{Strain}} \]

2. **Define Stress and Strain**:
- **Stress** is defined as force per unit area:
\[ \text{Stress} = \frac{\text{Force}}{\text{Area}} = \frac{F}{A} \]
- **Strain** is defined as the change in length divided by the original length:
\[ \text{Strain} = \frac{\Delta L}{L} \]

3. **Substituting Stress and Strain into Young's Modulus**:
We can substitute the definitions of stress and strain into the Young's modulus formula:
\[ Y = \frac{F/A}{\Delta L/L} = \frac{F \cdot L}{A \cdot \Delta L} \]

4. **Identify the Dimensions**:
- The dimension of force (F) is given by:
\[ [F] = MLT^{-2} \]
- The dimension of area (A) is:
\[ [A] = L^2 \]
- The dimensions of change in length (\(\Delta L\)) and original length (L) are both:
\[ [L] = L \]

5. **Combine the Dimensions**:
Now we can substitute these dimensions back into the equation for Young's modulus:
\[ Y = \frac{[F] \cdot [L]}{[A] \cdot [\Delta L]} = \frac{(MLT^{-2}) \cdot (L)}{(L^2) \cdot (L)} \]
Simplifying this gives:
\[ Y = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2} \]

6. **Final Result**:
Therefore, the dimensional formula for Young's modulus is:
\[ [Y] = ML^{-1}T^{-2} \]

### Conclusion:
The dimensional formula for Young's modulus is \( ML^{-1}T^{-2} \).

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