The longitudinal strain is only possible in

The correct option is Solids.

To understand why longitudinal strain is only possible in solids, let's break down the definitions of strain and the physical properties of states of matter:

1. What is Longitudinal Strain?
Longitudinal strain is defined as the ratio of the change in length ($\Delta L$) to the original length ($L$) of a body when it is subjected to a deforming force along its length. It is given by:
$\text{Longitudinal Strain}=\frac{\Delta L}{L}$

2. Conditions for Longitudinal Strain:
For a material to undergo longitudinal strain, it must possess a definite shape and length. When a stretching or compressing force is applied, the material must experience a restoring force that opposes this change in length, allowing it to maintain its structural integrity without flowing.

3. Comparing Solids, Liquids, and Gases:
• Solids: Solids have a definite shape, size, and volume due to strong intermolecular forces of attraction. When longitudinal stress is applied, a solid undergoes a change in length and exhibits longitudinal strain.
• Fluids (Liquids and Gases): Liquids and gases do not have a fixed shape or length. They take the shape of their container and flow when a shearing or longitudinal stress is applied. Because fluids cannot support longitudinal stress without flowing, they cannot exhibit longitudinal strain. They only exhibit volume (bulk) strain.

Therefore, longitudinal strain is possible only in solids.