Question

The volume of a wire remains unchanged when the wire is subjected to a certain tension. The poisson's ratio of the material of the wire is 0.25 0.3 0.4 0.5

Answer 1

The poisson's ratio of the material is 0.5

(d) is correct option

Explanation:

Given that,

The volume of a wire remains unchanged when the wire is subjected to a certain tension.

Let L be the length, r be the radius of the wire.

Volume of the wire is

$V=\pi r^2 L$

On differentiating both sides

$\Delta V=\pi(2r\delta r)L+\pi r^2\Delta L$

The volume of a wire remains unchanged.

Then, $0=\pi(2r\delta r)L+\pi r^2\Delta L$

$2\pi r L\Delta r+\pi r^2\Delta L=0$

$\dfrac{\dfrac{\Delta r}{r}}{\dfrac{\Delta L}{L}}=-\dfrac{1}{2}$

We need to calculate the poisson's ratio of the material

Using formula of poisson ratio

$\text{poisson's ratio}=-\dfrac{\text{Lateral strain}}{\text{longitudnal strain}}$

Put the value into the formula

$\text{poisson's ratio}=\dfrac{1}{2}$

$\text{poisson's ratio}=0.5$

Hence, The poisson's ratio of the material is 0.5.

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Topic : poisson's ratio

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