GATE (TF) Textile 2022 Question Paper Solution | GATE/2022/TF/49

Question 49 (Textile Technology & Fibre Science)

A take-up motion is shown below. The number of teeth on gear A, B, C, D and E are 60, 20, 40, 25 and 50, respectively. The circumference of the take-up roller is 40 cm. If one tooth is broken on gear B, then the wavelength (cm) of the fault in fabric (in integer) is ___.

gate textile 2022 question 49
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Given in the question-

Circumference of take-up roller=40 cm

No. of teeth in gear A(\ T_A)=60

No. of teeth in gear B(\ T_B)=20 and One teeth is broken on gear B

No. of teeth in gear C(\ T_C)=40

No. of teeth in gear D(\ T_D)=25

No. of teeth in gear E(\ T_E)=50

Here drive given to driven B by driver A, driven C by driver B ,driven D by driver C and driven E by driver D.

Since ,the fault is in the gear B,so that we will not consider gear A in default length and calculation will start from gear B.

Wavelength of the fault in fabric(\lambda)=\frac{T_B}{T_C}\times \frac{T_D}{T_E} \timescircumference of take up roller

Wavelength of the fault in fabric(\lambda)=\frac{20}{40}\times \frac{25}{50} \times 40

Wavelength of the fault in fabric(\lambda)=10 cm (Ans)

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