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The poisson’s ratio cannot have the value
A. $0.7$
B. $0.2$
C. $0.1$
D. $0.3$

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Last updated date: 21st Jul 2024
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Answer
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Hint: Poisson’s ratio has no unit because one quantity divided by another quantity with the same unit, so there is no unit for poisson’s ratio. Poisson's ratio is defined as the ratio of width per unit to change in length per unit. Poisson's ratio is transverse lateral strain to longitudinal strain in the direction of stretching force.

Complete step-by-step solution:
The poisson's ratio of stable, linear elastic material will be greater than one or less than $0.5$.
From young's modulus, the poisson's ratio is,
Let Y, K, n and $\sigma $are the young's modulus,
The ratio of modulus of rigidity and poisson's ratio respectively,
Therefore, $Y = 3K\left( {1 - 2\sigma } \right)$ it is standard formula
$Y = 2n\left( {1 + \sigma } \right)$ this also standard formula
Hence we get, $3K\left( {1 - 2\sigma } \right) = 2n\left( {1 + \sigma } \right)$
Now we are assuming that K, n are always positive, so that we can define in two cases,
Case(i): if $\sigma $is positive, then the right hand side is always positive. So, left hand side must be positive, therefore $2\sigma < 1$ or $\sigma < \dfrac{1}{2}$.
Case(ii): if $\sigma $ is negative, then the left hand side will always be positive, therefore $1 + \sigma > 0$ or $\sigma > - 1$.
Thus the intensity volume of poisson's ratio lies between $ - 1 < \sigma < 0.5$ from the requirement of young's modulus.
Most of the materials have poisson's ratio value ranging between $0$ to $0.5$,
Hence the correct option is $0.7$.

Note: The poisson's ratio is the ratio of longitudinal and lateral strain, the poisson's ratio cannot be less than one. The most common materials are thin in the cross section when it is stretched. The deformation of material in a direction perpendicular to the applied force is used for poisson's ratio measure.