GATE (TF) Textile 2020 Question Paper Solution | GATE/2020/TF/50

Question 50 (Textile Engineering & Fibre Science)

A cotton fibre has degree of cell wall thickening $(\theta)$ of 0.9 and perimeter of 40 $\mu m$ . The actual cross-sectional area of the wall $(\mu m^{2})$ of the fibre (rounded off to 1 decimal place) is __112.0 to 117.0__.

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Given:

Degree of cell wall thickening ( $(\theta)$ )=0.9

Perimeter(P)=40 $\mu m$ .

A’= $\frac{P^2}{4\pi }$

Formula:

$(\theta)$ =A/A’

Where, A is actual cross sectional area , A’ is standard cross sectional area and P is the perimeter

$(\theta)$ = $\frac{4\pi A}{P^2}$

$0.9 = \frac{4 \times 3.14 \times A}{40^2}$

$A = \frac{0.9 \times 40 \times 40}{4 \times 3.14}$

(Area)A=114.65 $(\mu m^{2})$ (Answer)

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