There is no change in the volume of a wire due to change in its length on stretching. The poisson's ratio of the material of the wire is

• A: 0.500
• B: −0.50
• C: +0.25
• D: −0.25

To determine the Poisson's ratio of the material of the wire, we need to understand the relationship between the change in length and volume when the wire is stretched. Poisson's ratio (ν) is defined as the negative ratio of transverse strain to axial strain.

Key Concepts

• Axial Strain: Change in length divided by original length.
• Transverse Strain: Change in diameter (or width) divided by original diameter.

In this case, since the volume of the wire does not change when it is stretched, it indicates that the material is incompressible in the lateral direction. This leads us to conclude that the transverse strain is equal to half of the axial strain.

Calculating Poisson's Ratio

The formula for Poisson's ratio is:

ν = - (Transverse Strain) / (Axial Strain)

Given that the volume remains constant, we can infer:

• If the axial strain is 1, the transverse strain would be -0.5 (indicating a reduction).

Thus, substituting these values into the formula gives:

ν = - (-0.5) / 1 = 0.5

Final Answer

The Poisson's ratio of the material of the wire is A: 0.500.