GATE (TF) Textile 2005 Question Paper Solution | GATE/2005/TF/71

In an idealized helical yarn of 20 tex, the twist is 10 turns/cm. The surface twist angle is 32^o.

The approximate specific volume (cc/g) of the above yarn is

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Option C

Tex=20

Ne=590.5/20

Ne=29.51

TPCM=10

$\theta=32^o$

Specific volume of the yarn(V)=?

By formula-

$tan \theta=\pi \times D \times TPCM$

$tan 32=3.14\times D \times 10$

$0.624=3.14\times D \times 10$

D=0.0198 cm

D=0.198 MM

D=0.2 mm

D=0.02/2.54 inch

D=0.0079 inch

By formula-

$D=0.99 \times \sqrt \frac{V} {840 \times Ne}$ inch

$0.0079=0.99 \times \sqrt \frac{V} {840 \times 29.51}$

$\frac{0.0079}{0.99}= \sqrt \frac{V} {24788.4}$

$0.00798= \sqrt \frac{V} {24788.4}$

Square both side-

$0.00798^2=( \sqrt \frac{V} {24788.4})^2$

$0.00000637=\frac{V} {24788.4}$

$0.0000637 \times 24788.4=V$

V=1.57 cm3/g (Ans)