Volume of a wire of radius r and length l is,
V=πr
2
l
∴dV=2πrldr+πr
dl
0=2πrldr+πr
(dv=0, as volume is unchanged)
∴2rldr=−r
r
dr
=−
1
∴
∴σ=−
As, here −ve sign implies that if, length increased, radius decreased, so, we can write
σ=
=0.5
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Answers & Comments
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