GATE (TF) Textile 2014 Question Paper Solution | GATE/2014/TF/47

Question 47 (Textile Engineering & Fibre Science)

The breaking load of a 300 mtex fibre is 110mN. If the density of the fibre is 1.24 g/cm3, breaking stress in kN/cm2, accurate to one decimal place, will be …………………..

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Given in the question–
Breaking load=110 mN
=110*10-3 N

Fineness of fibre=300 mtex
=300*10-3 tex
Density of fibre=1.24 g/cm3

Breaking stress(kN/cm2)=?

Formula:

Breaking stress=Breaking load/Unit Area

By definition of tex-
Fineness of fibre=300*10-3 tex

i.e.,
1000 meter length have=300*10-3 gm

1 meter length have=300*10-3/1000

Hence,
Fibre fineness( gm/m)=300*10-3/1000

Fibre fineness( gm/cm)=300*10-3/(1000*100)

Fibre fineness( gm/cm)=300*10-3/105

Fibre fineness/Density of fibre=\frac{\frac{300\times 10^-3}{100000}}{1.24}

Fibre fineness/Density of fibre=\frac{300\times 10^-3}{100000\times 1.24}

Fibre fineness/Density of fibre=242 x 10-8 cm2

Now,
Breaking stress=Breaking load/Unit Area

Breaking stress=110*10-3/242*10-8

Breaking stress=0.4545*105 N/cm2

Breaking stress=0.4545*105/1000 kN/cm2

Breaking stress=0.4545*102 kN/cm2

Breaking stress=45.45 kN/cm2

Breaking stress=45 kN/cm2 (Answer,up to one decimal)

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