GATE (TF) Textile 2022 Question Paper Solution | GATE/2022/TF/31

Question 31 (Textile Technology & Fibre Science)

Keeping the speed of all other components of a carding machine unchanged, the angular velocity of a cylinder with damaged wire points in an area of 2 cm x 2 cm is doubled. Wavelength of the periodic fault in the card sliver would be

(A)	Same
(B)	Halved
(C)	Doubled
(D)	Tripled

[Show Answer]

Let us assume, the initial angular velocity of the cylinder(v1) =v

Then, Final angular velocity of the cylinder(v2)=2v

By formula;

Wavelength of the periodic fault( $\lambda$ ) is inversaly propotional to angular velocity of the carding cylinder

$\frac{\lambda_1}{\lambda_2}=\frac{v_2}{v_1}$

$\frac{\lambda_1}{\lambda_2}=\frac{2v}{v}$

$\frac{\lambda_1}{\lambda_2}=\frac2$

$\lambda_1=2\times\lambda_2$

$\lambda_2=\frac{\lambda_1}{2}$

Wavelength of the periodic fault in the card sliver would be halved. (Ans)

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