For the different materials it is given that `Y_(1) gt Y_(2)` and `B_(1) lt B_(2)`. Here, Y is Young's modulus of elasticity and B, the Bulk modulus of elasticity. Then we can conclude that

Options

A. 1 is more ductile
B. 2 is more ductile
C. 1 is more malleable
D. 2 is more malleable

Answer

To solve the problem, we need to analyze the given information about Young's modulus (Y) and Bulk modulus (B) for two different materials.

### Step-by-Step Solution:

1. **Understanding Young's Modulus (Y)**:
- Young's modulus is a measure of the stiffness of a solid material. It is defined as the ratio of tensile stress to tensile strain.
- A higher Young's modulus indicates that the material is stiffer and less deformable under tensile stress.

2. **Understanding Bulk Modulus (B)**:
- Bulk modulus is a measure of a material's resistance to uniform compression. It is defined as the ratio of volumetric stress to the change in volume strain.
- A lower Bulk modulus indicates that the material is more compressible.

3. **Given Information**:
- We have two materials with the following properties:
- \( Y_1 > Y_2 \) (Material 1 has a higher Young's modulus than Material 2)
- \( B_1 < B_2 \) (Material 1 has a lower Bulk modulus than Material 2)

4. **Analyzing Young's Modulus**:
- Since \( Y_1 > Y_2 \), Material 1 is stiffer than Material 2. This means that Material 1 is less malleable (more rigid) compared to Material 2.

5. **Analyzing Bulk Modulus**:
- Since \( B_1 < B_2 \), Material 1 is more compressible than Material 2. This means that Material 1 is less resistant to compression compared to Material 2, which indicates that Material 1 is more ductile.

6. **Conclusion**:
- From the analysis, we can conclude that:
- Material 1 is less malleable (due to higher Young's modulus) and more ductile (due to lower Bulk modulus).
- Material 2 is more malleable (due to lower Young's modulus) and less ductile (due to higher Bulk modulus).

### Final Conclusion:
- Material 1 is stiffer and more ductile, while Material 2 is more malleable and less ductile.