GATE (TF) Textile 2022 Question Paper Solution | GATE/2022/TF/46

Question 46 (Textile Technology & Fibre Science)

Nine slivers having same mean linear density are doubled on a drawframe. If the standard deviation of linear density of each sliver is 0.3 ktex, then the standard deviation (ktex) of linear density of the doubled sliver (correct up to 1 decimal place) is _.

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Given in the question-

Stadard deviation of single sliver( $\sigma_1$ )=0.3 ktex

Number of single slivers( $N_1$ )=9

Stadard deviation of double sliver( $\sigma_2$ )=?

Number of double sliver( $N_2$ )=81

Now by formula,

$N=(\frac{1.96\times CV}{SE})^2$

N(Number of samples) is directly proportional to the square of CV(Coefficient of variation)

$\frac{N_1}{N_2}=(\frac{CV_1}{CV_2})^2$

and formula of $CV=standard deviation(\sigma)/mean value(X)$

$\frac{9}{81}=(\frac{\sigma_1}{\sigma_2})^2$

$\frac{1}{9}=(\frac{0.3}{\sigma_2})^2$

$\frac{1}{3}=\frac{0.3}{\sigma_2}$

$\sigma_2=0.3\times 3$

$\sigma_2=0.9$ (Ans)

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Frequently Asked Questions | FAQs

What is linear density ?

Linear density is a measure of the mass per unit length of a material. It is commonly used to describe the diameter of a fiber, yarn, or filament. Linear density is often expressed in units of denier (for fibers) or tex (for yarns), where the larger the value, the thicker the material. For example, a high linear density fiber or yarn will have a larger diameter and be heavier per unit length than a low linear density fiber or yarn of the same material. Linear density is an important property in many applications, as it affects the strength, flexibility, and appearance of the material. For example, in the textile industry, linear density is used to determine the right balance of strength and drapability in a fabric, while in the fishing industry, linear density affects the sensitivity and strength of fishing line.

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