GATE (TF) Textile 2018 Question Paper Solution | GATE/2018/TF/53

Question 53 (Textile Technology & Fibre Science)

The bending length of a nonwoven fabric in machine direction is two times the bending length in cross-machine direction. The ratio of flexural rigidities of this fabric in machine direction to cross-machine direction is __8__.

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Given in the question–

Let , blending length of fabric in cross machine direction(L₂)=L

Then, blending length in the machine direction(L₁)=2L

Let , flexural regidity in machine direction=G₁

Then, flexural regidity in cross machine direction=G₂

G₁/G₂=?

Formula:

Flexural regidity(G)=W x C³

Where, C is the bending length

i.e.
$G \alpha C^3$

hence , G is directly proportional to the cube of the bending length

$\frac{G_1}{G_2}=\frac{(Blending length in cross machine direction)^3}{(Blending length in the machine direction)^3}$

$\frac{G_1}{G_2}=\frac{(L_1)^3}{(L_2)^3}$

$\frac{G_1}{G_2}=\frac{(2L)^3}{(L)^3}$

$\frac{G_1}{G_2}=\frac{(2)^3\times(L)^3}{(L)^3}$

$\frac{G_1}{G_2}=8$ (Answer)

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