Out of solids , liquids and gases, which one has all the three types of modulus ofelasticity and why gases have only bulk modulus of elasticity.

Options

A. Solids
B. Liquids
C. Gases
D. Both solids and liquids

Explanation

To solve the question, we need to analyze the properties of solids, liquids, and gases in relation to the three types of modulus of elasticity: Young's modulus, Shear modulus, and Bulk modulus.

### Step-by-Step Solution:

1. **Understanding Modulus of Elasticity**:
- The modulus of elasticity is a measure of a material's ability to deform under stress. There are three main types:
- **Young's Modulus**: Measures the tensile or compressive stress in a material.
- **Shear Modulus**: Measures the material's response to shear stress.
- **Bulk Modulus**: Measures the material's response to uniform pressure applied in all directions.

2. **Analyzing Solids**:
- Solids can undergo changes in length (tension/compression), changes in shape (shear), and changes in volume (compression). Therefore, solids can exhibit all three types of modulus of elasticity:
- Young's modulus (for length change)
- Shear modulus (for shape change)
- Bulk modulus (for volume change)

3. **Analyzing Liquids**:
- Liquids can change volume when subjected to pressure, but they do not have a defined shape and cannot resist shear stress. Therefore, they primarily exhibit Bulk modulus but do not have Young's modulus or Shear modulus.

4. **Analyzing Gases**:
- Gases can also change volume under pressure, but like liquids, they do not have a defined shape and cannot resist shear stress. Thus, gases only exhibit Bulk modulus of elasticity. They cannot have Young's modulus or Shear modulus because they cannot maintain a fixed shape or resist shear forces.

5. **Conclusion**:
- Out of solids, liquids, and gases, **solids** have all three types of modulus of elasticity (Young's modulus, Shear modulus, and Bulk modulus) because they can change in length, shape, and volume. **Gases**, on the other hand, only have the Bulk modulus of elasticity because they can only change in volume and do not resist shear or maintain a fixed shape.

### Final Answer:
- **Solids** have all three types of modulus of elasticity, while **gases** have only the Bulk modulus of elasticity.