# GATE (TF) Textile 2007 Question Paper Solution | GATE/2007/TF/78

A 46 mm diameter rotor is spinning 60 tex yarn at 100 m/min. The trash level in feed sliver is 0.2%. The opening roller can clean the sliver to the extent of 70%. The self cleaning effect of the yarn arm within the rotor is 50%

###### Question 78 (Textile Engineering & Fibre Science)

trash deposition (mg/cm of rotor circumference) after 1 min will be

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Option A is correct.

Rotor dia=46mm

Yarn count=60 tex

Rotor speed=100 m/min

Trash level in feed sliver=0.2%

Cleaning % of opening roller=70%

Self cleaning effect of the yarn within the rotor=50%

Trash deposition (mg/cm of rotor circumference) after 1 min=?

Rotor circumference=0.1444 m

Rotor circumference=14.44 cm

Now,

By definition of tex-

By unitary rule-

1000 meter length have..=60 gm weight

1 m have……………………………=60/1000

Similarily,

100 m length have…………….=60 x 100/1000

Weight of yarn=6 gm

Weight of output yarn=6 x (Trash level% in feed sliver) x (1-Cleaning % of opening roller) x (1-Self cleaning effect %of the yarn within the rotor)

Weight of output yarn=6 x (0.2%) x (1-70%) x (1-50%)

Weight of output yarn=6 x (0.002) x (1-0.70) x (1-0.50)

Weight of output yarn=6 x 0.002 x 0.30 x 0.50

Weight of output yarn=0.0018 gm

Weight of output yarn=1.8 mg

Trash deposition (mg/cm of rotor circumference) =Weight of output yarn/Rotor circumference

Trash deposition (mg/cm of rotor circumference) =1.8/14.44

Trash deposition (mg/cm of rotor circumference) =0.1246 (Ans)