According to Hooke's law, within the elastic limit stress/strain `=` constant. This constant depends on the type of strain or the type of force acting. Tensile stress might result in compressional or elongative strain, however, a tangential stress can only cause a shearing strain. After crossing the elastic limit, the material undergoes elongation and beyond a stage beaks. All modulus of elasticity are basically constants for the materials under stress.
If stress/strain is `x` in elastic region and `y` in the region of yield, then

Options

A. `x=y`
B. `xgty`
C. `xlty`
D. `x=2y`

Explanation

To solve the question regarding the relationship between stress and strain according to Hooke's law, we will follow these steps:

### Step 1: Understand Hooke's Law
Hooke's law states that within the elastic limit of a material, the stress applied to it is directly proportional to the strain produced. This can be mathematically expressed as:
\[ \text{Stress} = k \times \text{Strain} \]
where \( k \) is the modulus of elasticity.

### Step 2: Define the Modulus of Elasticity
The modulus of elasticity (M) is defined as the ratio of stress to strain:
\[ M = \frac{\text{Stress}}{\text{Strain}} \]
In the elastic region, we denote this ratio as \( x \):
\[ x = \frac{\text{Stress}}{\text{Strain}} \text{ (in elastic region)} \]

### Step 3: Analyze the Yield Point
When the material reaches the yield point, it begins to deform plastically. The ratio of stress to strain in this region is denoted as \( y \):
\[ y = \frac{\text{Stress}}{\text{Strain}} \text{ (in yield region)} \]

### Step 4: Compare x and y
As stress increases, strain also increases. Initially, this relationship is linear (in the elastic region). However, after reaching the yield point, the material's response becomes non-linear, and the slope of the stress-strain curve decreases. Therefore, the modulus of elasticity in the yield region (y) is less than that in the elastic region (x):
\[ x > y \]

### Conclusion
Thus, we conclude that the value of \( x \) (modulus of elasticity in the elastic region) is greater than the value of \( y \) (modulus of elasticity in the yield region).

### Final Answer
\[ x > y \]

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