GATE (TF) Textile 2017 Question Paper Solution | GATE/2017/TF/49

Question 49 (Textile Engineering & Fibre Science)

The compressive pressure applied on to a fabric is inversely proportional to the cube of thickness of the fabric. If the thickness is halved during compression, then the pressure increases by __6.9 to 8.1__ times.

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Given in the question–
Let , inial thickness of the fabric=t₁

Then, final thickness of the fabric(t₂)=t₁/2
and
Initial compressive pressure applied on fabric=P₁

Final compressive pressure applied on fabric(P₂)=?

Given,compressive pressure is inversaly proportional to the cube of the thickness of the fabric

$Compressive pressure \alpha \frac{1}{(thickness)^3}$

$P \alpha \frac{1}{(t)^3}$
i.e.,

$\frac{P_1}{P_2}=\frac{t_2^3}{t_1^3}$

$\frac{P_1}{P_2}=\frac{\frac{t_1}{2}^3}{t_1^3}$

$\frac{P_1}{P_2}=\frac{1}{8}$

$\frac{P_1}{P_2}=\frac{1}{8}$

$\frac{P_2}{P_1}=\frac{8}{1}$

$P_2=8 \times P_1$

i.e. final pressure is increased by 8 times. (Answer)

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