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Question

Physics Question on Gravitation

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

-0.5

C

0.25

D

-0.25

Answer

0.5

Explanation

Solution

Let the material of length 1 and side s If a material maintains constant volume during stretching V=1×s2V = 1 \times s ^{2}
Differentiate wrt dl dV=s2⋅dl+1.2s⋅dsd V = s ^{2} \cdot d l + 1 . 2 s \cdot d s
dl.s == 2l.ds dsdl=−12s1\frac{d s}{d l}=-\frac{1}{2} \frac{s}{1}
η=−dssdl1=12\eta=-\frac{\frac{d s}{s}}{\frac{d l}{1}}=\frac{1}{2}