GATE (TF) Textile 2009 Question Paper Solution | GATE/2009/TF/06

Question 06 (Textile Engineering & Fibre Science)

Ring spun cotton yarn of 30, 40, 50 and 60 tex are made from the same fibre. All these yarns are spun with a constant twist per cm of 10. The yarns can be arranged in descending order of helix angle of surface fibres as

(A)	30, 60, 50, 40
(B)	40, 60, 50, 30
(C)	30, 40, 50, 60
(D)	60, 50, 40, 30

[Show Answer]

Option D is correct

All have same twist per cm.

By the formula-

$tan\alpha=0.0112\times V_y^\frac{1}{2}\times TM$

and we know,

$TPI=TM\sqrt count$

$tan\alpha=0.0112\times V_y^\frac{1}{2}\times TPM \times \sqrt count(tex)$

i.e,
$tan\alpha$ is directly proportional to the square root of count(tex).

So,that
If number of count increases,surface helix increases.

Hence ,60s tex cotton fibre have maximum surface helix angle.

The descending order of helix angle of surface fibres-

60,50,40,30 (Ans)

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