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There is no change in the volume of a wi...

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

`0.5`

B

`-0.50`

C

`0.25`

D

`-0.25`

Text Solution

Verified by Experts

The correct Answer is:
b
If the length of wire increases, then radius of wire decreases. Poisson's ratio
`sigma ("lateral strain")/("longitudianl strain") = - (Delta R//R)/(Delta I // I) = - (Delta R)/(R ) xx (I)/(Delta I)`
Let D be the diameter and V be the volume. Then,
`V = pi D^(2) L//4`
There is no change in volume
`:. 0 = pi 2 D dD L + pi D^(2) dL`
or `((dD//D))/((dL//L)) = - 0.5`
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