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

Question

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) 0.50 (B) -0.50 (C) 0.25 (D) -0.25

Tardigrade Admin · Accepted Answer

Let the material of length 1 and side s If a material maintains constant volume during stretching

V = 1 \times s^{2}

Differentiate wrt dl

d V = s^{2} \cdot d l + 1.2 s \cdot d s

dl.s

=

2l.ds

\frac{d s}{d l} = - \frac{1}{2} \frac{s}{1}

η = - \frac{\frac{d s}{s}}{\frac{d l}{1}} = \frac{1}{2}

Q. 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

0.50

-0.50

0.25

-0.25

Let the material of length 1 and side s If a material maintains constant volume during stretching V=1×s2 Differentiate wrt dl dV=s2⋅dl+1.2s⋅ds dl.s = 2l.ds dlds​=−21​1s​ η=−1dl​sds​​=21​