Question

if change in length of wire on strecrhing it is 1% and Poisson's ratio is 1/4 then % change in volume​

Answer 1

Volume of a wire of radius r and length l is,

V=πr

2

l

∴dV=2πrldr+πr

2

dl

0=2πrldr+πr

2

dl

(dv=0, as volume is unchanged)

∴2rldr=−r

2

dl

r

dr

=−

2

1

l

dl

∴

l

dl

r

dr

=−

2

1

∴σ=−

2

1

As, here −ve sign implies that if, length increased, radius decreased, so, we can write

σ=

2

1

=0.5