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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

`0.500`

B

`-0.50`

C

`+0.25`

D

`-0.25`

Text Solution

Verified by Experts

The correct Answer is:
A
`V = (pi D^(2) L)/(4) :. dV = pi. 2D AD.L + pi D^(2) . Delta L = 0`
`:. 2 Delta D L = - D Delta L :. (Delta D)/(D) = -(1)/(2)(Delta L)/(L)`
`:. sigma = (Delta D)/(D)//(Delta L)/(L) = -(1)/(2)`
This is the theoritical value but `sigma` cannot be negative because when L increases, D decreases. `:. sigma = 0.5`
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