GATE (TF) Textile 2017 Question Paper Solution | GATE/2017/TF/39

Question 39 (Textile Engineering & Fibre Science)

A T-shirt is produced from cotton fibre of 1520 kgm-3 density, 1.4 dtex fitness and 30 mm length. The total number of fibres in the T-shirt of 0.15 kg is __34 to 37__x106.

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Given in the question
Density of cotton fibre=1520 kgm-3

Fineness of fibre=1.4dtex
=0.14 tex

Length of fibre=30 mm
=30*10-3 meter

Weight of T-shirt=0.15 kg
=0.15*103 gm

Number of fibres in the T-shirt=?


Number of fibres=Weight of T-shirt/Weight of fibre

Tex=0.15 tex
By unitary rule:
1000 meter length have=0.14 gm weight

1 meter length have=0.14/1000

Then, 30*10-3 meter length have=0.14*30*10-3/1000

Weight of fibre=4.2*10-6 gm

Number of fibres=0.15*103/4.2*10-6

Number of fibres=35.71*106 (Answer)

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