The longitudinal extension of any elastic material is very small. In order to have an appreciable change, the material must be in the form of

The correct option is Long thin wire.

To understand why a long thin wire undergoes the most noticeable longitudinal extension, we can analyze the relationship between the applied force and the resulting change in length using Young's modulus of elasticity ($Y$).

Young's modulus ($Y$) is defined as the ratio of tensile stress to tensile strain:

$Y=\frac{\text{Stress}}{\text{Strain}}=\frac{F/A}{\Delta L/L}$

Here:

• $F$ is the applied deforming force,
• $A$ is the cross-sectional area of the material,
• $L$ is the original length of the material, and
• $\Delta L$ is the longitudinal extension (change in length).

Rearranging the equation to solve for the extension ($\Delta L$):

$\Delta L=\frac{F\cdot L}{A\cdot Y}$

For a given material (where $Y$ is constant) and a constant applied force ($F$), the longitudinal extension is:

1. Directly proportional to the original length of the material:

$\Delta L\propto L$

2. Inversely proportional to the cross-sectional area:

$\Delta L\propto \frac{1}{A}$

Therefore, to obtain a large and appreciable change in length ($\Delta L$), the material should have a large length ($L$) and a very small cross-sectional area ($A$). This configuration corresponds directly to a long thin wire.