GATE (TF) Textile 2013 Question Paper Solution | GATE/2013/TF/42

Question 42 (Textile Engineering & Fibre Science)

On a winding machine, if the winding speed is increased from 1000 m/min to 1200 m/min, the percentage increase in the yarn tension will be approximately

(A)	12
(B)	24
(C)	36
(D)	44

Answer / Solution

Given in the question–
Winding initial speed(v₁)=1000 m/min

Winding final speed(v₂)=1200 m/min

The percentage increased in yarn tension( $\Delta T$ )=?

By formula:

$Tension \alpha speed^2$

Yarn tension is directly proportional to the square of the speed.

$T \alpha v^2$

$\frac{T_1}{T_2}=\frac{v_1^2}{v_2^2}$

$\frac{T_1}{T_2}=\frac{1000^2}{1200^2}$

$\frac{T_1}{T_2}=\frac{1000000}{1440000}$

$\frac{T_1}{T_2}=\frac{100}{144}$

$\frac{T_2}{T_1}=\frac{144}{100}$

$\frac{T_1}{T_2}-1=\frac{144}{100}-1$

$\frac{T_1}{T_2}-1=1.44-1$

$\frac{T_1}{T_2}-1=0.44$

$(\frac{T_1}{T_2}-1)\times 100=0.44 \times 100$

$(\frac{T_1}{T_2}-1)\times 100=44%$

$\Delta T=44%$

i.e., The percentage increase in the yarn tension=44 (Answer)
Option D is correct.