Let `Y_(s)` and `Y_(A)` represent Young's modulus for steel and aluminium respectively. It is said that steel is more elastic than aluminium.Therefore, it follows that

Options

A. `Y_(s) =Y_(A)`
B. `Y_(s) lt Y_(A)`
C. `Y_(s) gt Y_(A)`
D. `(Y_(S))/(Y_(A)) = 0`

Explanation

To solve the problem, we need to analyze the relationship between Young's modulus and the elasticity of materials. Here's a step-by-step breakdown:

### Step 1: Understand Young's Modulus
Young's modulus (Y) is defined as the ratio of stress to strain in a material. Mathematically, it is expressed as:
\[ Y = \frac{\text{Stress}}{\text{Strain}} \]
Where:
- Stress \( = \frac{F}{A} \) (Force per unit area)
- Strain \( = \frac{\Delta L}{L} \) (Change in length per original length)

### Step 2: Define Elasticity
Elasticity refers to the ability of a material to return to its original shape after the removal of a load. A material is considered more elastic if it deforms less under the same applied stress.

### Step 3: Compare Steel and Aluminium
The problem states that steel is more elastic than aluminium. This means that when the same force is applied to both materials, steel will experience less deformation (elongation) compared to aluminium.

### Step 4: Relate Elasticity to Young's Modulus
Since steel is more elastic, it will have a smaller strain for the same stress compared to aluminium. Therefore, we can conclude:
- If \( \Delta L_s \) is the elongation in steel and \( \Delta L_a \) is the elongation in aluminium, then:
\[ \Delta L_s < \Delta L_a \]

### Step 5: Express Young's Modulus for Both Materials
Using the definition of Young's modulus:
- For steel:
\[ Y_s = \frac{F/A}{\Delta L_s/L} \]
- For aluminium:
\[ Y_a = \frac{F/A}{\Delta L_a/L} \]

### Step 6: Analyze the Relationship
Since \( \Delta L_s < \Delta L_a \), it follows that:
\[ Y_s > Y_a \]
This means that the Young's modulus for steel is greater than that for aluminium.

### Conclusion
From the analysis, we conclude that:
\[ Y_s > Y_a \]

### Final Answer
Therefore, the correct option is:
**\( Y_s > Y_a \)**

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