GATE (TF) Textile 2014 Question Paper Solution | GATE/2014/TF/40

Question 40 (Textile Engineering & Fibre Science)

The surface helix angle of a fibre in a yarn of 0.3 mm diameter is 30o. Assuming ideal helix geometry, the helix angle (in degrees), of a fibre situated at 0.1 mm from the yarn axis, accurate to one decimal place, will be …………………

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Given in the question
Fibre dia(D)=0.3 mm

Helix angle of a fibre in a yarn(\alpha)=30o

Fibre situation(d)=0.1 mm

Helix angle(\theta) =?

By helix geometry

tan\alpha=2\times \pi D
tan\theta=2\times \pi d

\alpha is helix angle and D is diameter

By deviding both equetions.

We get,

\frac{tan \alpha}{tan \theta}=\frac{D}{d}

\frac{tan 30^o}{tan \theta}=\frac{0.3}{0.1}

\frac{tan 30^o}{tan \theta}=\frac{0.3}{0.1}

\frac{0.577}{tan \theta}=\frac{0.3}{0.1}

\frac{0.577\times 0.1}{0.3}=tan \theta

0.192=tan \theta

tan \theta=0.192


\theta=10.87^o (Answer)

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