GATE (TF) Textile 2016 Question Paper Solution | GATE/2016/TF/43

Question 43 (Textile Engineering & Fibre Science)

The crimp % of a square cloth in which thread spacing is equal to the yarn diameter and no jamming takes place, will be __56 : 57__.

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Given in the question:

Given :

P=D

Where, thread spacing =P

Dia of yarn=D

Formula:

P=Dsin $\theta$
Here,
P=D
Then,
Sin $\theta$ =1

$\theta=Sin^-1 1$

$\theta=90^o$

or

$\theta=\frac{\pi}{2}$

By formula:;

$Crimp percentage=\frac{l-P}{P}\times100$

$Crimp percentage=\frac{D\theta-DSin\theta}{DSin\theta}\times100$

$Crimp percentage=\frac{\theta-Sin\theta}{Sin\theta}\times100$

$Crimp percentage=\frac{(\frac{\pi}{2})-Sin(\frac{\pi}{2})}{Sin(\frac{\pi}{2})}\times100$

$Crimp percentage=\frac{(\frac{3.14}{2})-1}{1}\times100$

$Crimp percentage=\frac{(1.57)-1}{1}\times100$

$Crimp percentage=\frac{(0.57}{1}\times100$

$Crimp percentage=0.57\times100$

Crimp percentage=57 (Answer)

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