Question

if poissons ratio is 0.5 and increase in length of wire on stretching is 0.08% then the diameter is reduced by
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Answer 1

If poissons ratio is 0.5 and increase in length of wire on stretching is 0.08% then the diameter is reduced by  0.025%

Explanation:

Given:

Poisson's ratio 0.5

Increase in length of wire on stretching 0.08%

To find out:

the reduction in diameter

Solution:

We know that

Poisson's ratio = -(Lateral Strain)/(Longitudinal Strain)

Here, longitudinal strain = 0.05%

Therefore,

Lateral Strain = -0.5 × 0.05% = -0.025%

Here lateral strain will cause the reduction in diameter

Negative sign means that the diameter is reducing

Hope this answer is helpful.

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Answer 2

Given:

Poisson's ratio, σ = 0.5

Increase in length, ΔL = 0.08 %

To Find:

The decrease in the diameter, i.e., ΔD

Calculation:

- Longitudinal strain = ΔL/L = 0.08% of L/L = 0.0008

- The Poisson's ratio is given as:

Poisson's ratio =  -(Lateral Strain)/(Longitudinal Strain)

⇒ σ = -(ΔD/D)/(ΔL/L)

⇒ 0.5 = -(ΔD/D)/0.0008

⇒ (ΔD/D) = - 0.5 × 0.0008

⇒ (ΔD/D) = - 0.0004

⇒ ΔD = - 0.04 % of D

- So, the diameter is reduced by 0.04 % of the original diameter.