GATE (TF) Textile 2022 Question Paper Solution | GATE/2022/TF/52

Question 52 (Textile Technology & Fibre Science)

For a wool fibre strand, the relationship between $V_r$ (limit CV % of linear density) and $N$ (average number of fibres in the cross-section of the strand) is given below.

$V_r = \frac{112}{\sqrt{N}}$

[Show Answer]

Given in the question-

$V_r = \frac{112}{\sqrt{N}}$

Where $V_r$ is the CV% limit of wool fibre strand and N is the average number of fibres in the cross-section

By the formula-

$V_r^2=\frac{100^2}{N}+\frac{V_s^2}{N}$

Where $V_s$ is the Limit CV% of linear density of wool fibre

${\frac{112^2}{\sqrt{N}^2}=\frac{100^2}{N}+\frac{V_s^2}{N}$

$\frac{112^2}{N}=\frac{100^2}{N}+\frac{V_s^2}{N}$

$\frac{12544}{N}=\frac{10000}{N}+\frac{V_s^2}{N}$

$12544=10000+V_s^2$

$V_s^2=12544-10000$

$V_s^2=2544$

$V_s=\sqrt (2544)$

$V_s=50.44$

(Ans)

Previous Question

Next Question

Frequently Asked Questions | FAQs

GATE Textile Engineering and Fibre Science (TF) Question Papers | GATE Textile Question Answer | GATE Textile Solved Question Papers | GATE Textile Papers | GATE Textile Answer Key