The Poisson’s ratio of the material is 0.5. If a force is applied to a wi

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The Poisson’s ratio of the material is 0.5. If a force is applied to a wire of this material, there is a decrease in the cross sectional area by 4%. The percentage increase in its length is

Options:

A . 1%

B . 2%

C . 2.5%

D . 4%

Answer: Option D
:
D
Given Poisson's ration= 0.5
It shows that the density of material is constant
Therefore the change in volume of the wire is zero
Thus

V = A \times l

=constant
log V=log A+log |
therefore

\frac{△ V}{V} = 0 = \frac{△ A}{A} + \frac{△ l}{l}

\frac{△ l}{l} = - \frac{△ A}{A}

or % increase in length=

\frac{△ l}{l} \times 100

=-(-4)
=4%

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