GATE (TF) Textile 2018 Question Paper Solution | GATE/2018/TF/52

Question 52 (Textile Technology & Fibre Science)

The theoretical limit coefficient of variation (Vr in %) of the weight per unit length of cotton sliver is $V_r=\frac{106}{\sqrt{N}}$ , where N is the average number of fibres present in the crosssection of the sliver. To derive this expression, the coefficient of variation (in %) of the fibre weight per unit length, accurate to two decimal places, is considered as __35.00 to 36.00__.

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$V_r=\frac{106}{\sqrt{N}}$ ,
Then,
$V_r^2=\frac{106^2}{N}$

where N is the average number of fibres present in the cross section of the sliver.

CV of fibre weight per unit length( $V_m$ )=?

Formula:
$V_r^2=\frac{100^2}{N}+\frac{V_m^2}{N}$

Where,
$V_r$ =coefficient of variation of weight per unit length of cotton sliver

$V_m$ =coefficient of variation of weight per unit length of cotton fibre

N=Avg number of fibres

$\frac{106^2}{N}=\frac{100^2}{N}+\frac{V_m^2}{N}$

$\frac{106^2}{N}=\frac{100^2}{N}+\frac{V_m^2}{N}$

$\frac{106^2}{N}=\frac{100^2+V_m^2}{N}$

$106^2=100^2+V_m^2$

$11236=10000+V_m^2$

$11236-10000=V_m^2$

$1236=V_m^2$

$\sqrt1236=V_m$

$13.16=V_m$

$V_m=13.16$ (Answer)