GATE (TF) Textile 2018 Question Paper Solution | GATE/2018/TF/49

Question 49 (Textile Technology & Fibre Science)

The diameter and length of torsion rod used in a projectile loom are increased by 5% and 20%, respectively. If the torque required to twist the rod increases by X%, then the value of X, accurate to two decimal places, is __1.27 to 1.31__.

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Let ,initial diameter of torsional rod=d1

Then, final diameter of torsional rod(d2)=d1+d1 x 5%
d2=d1+(d1 x 5/100)
d2=d1+d1 x 0.05

d2=1.05 x d1

Let, initial length of torsional rod=l1

Then, final length of torsional rod(l2)=l1+l1 x 20%
l2=l1+(l1 x 20/100)
l2=l1+0.20 x l1

l2=1.2 xl1

Let, initial torque required to twist the rod=\tau_1

Then, final torque required to twist the rod(\tau_2)=\tau_1+(\tau_1\times X%)


By formula:


Where, \tau is torque , d is diameter of rod and l is length of torsional rod



\frac{\tau_1}{(1+0.01X)\tau_1}=\frac{d_1^4}{(1.05)^4\times d_1^4}\times\frac{1.2\times l_1}{l_1}

\frac{\tau_1}{(1+0.01X)\tau_1}=\frac{d_1^4}{1.22\times d_1^4}\times\frac{1.2\times l_1}{l_1}

\frac{1}{1+0.01X}=\frac{1}{1.22}\times\ 1.2

\frac{1}{1+0.01X}=\frac{1}{1.22}\times\ 1.2











X=1.70 (Answer)

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