GATE (TF) Textile 2008 Question Paper Solution | GATE/2008/TF/65

When denier of a fibre is doubled, its diameter increases by

[Show Answer]

Option B is correct.

Given in the question-

Let,
Initial denier of fibre(D1)=D

Then, final denier of fibre(D2)=2D

Its diameter increased by=?

By formual-

$Dia=4.44 \times 10^-3 \sqrt \frac{Denier}{density of fibre}$

Hence,

Dia is directly proportional to the square root of the denier of fibre.

$Dia \alpha \sqrt denier of fibre$

$\frac {d_1}{d_2}=\sqrt\frac{D_1}{D_2}$

$\frac {d_1}{d_2}=\sqrt\frac{D}{2D}$

$\frac {d_1}{d_2}=\sqrt\frac{1}{2}$

$\frac {d_2}{d_1}=\sqrt 2$

$\frac {d_2}{d_1}=1.41$

d2=1.41d1
I.e,

Increase in fibre diameter=1.41 times (Ans)