GATE (TF) Textile 2011 Question Paper Solution | GATE/2011/TF/46

If the error in the measurement of the diameter of a yarn is 0.5%, the error in the estimated cross-sectional area of this yarn would be

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Given in the question-

Error in the measurement of the diameter of yarn=0.5%

Then, error in the estimated cross-sectional area of this yarn would be=?

By the formula-

Area of cylinder(yarn cross-section)= ${2 \times \pi \time D^2}{4}$

Area of cylinder(yarn cross-section) $\alpha D^2$

Cross-sectional area of yarn is directly proportional to the square of the diameter of the yarn

Now,

$[\frac{\Delta A}{A} \times 100]=2[\frac{\Delta D}{D} \times 100]$

i.e , percentage error in cross-sectional area of yarn is twice the percentage error of the diameter of the yarn.

Where,
$\Delta A=(A_2-A_1)$ and

$\Delta D=(D_2-D_1)$

Percentage error in cross-sectional area of yarn= $2 \times [0.5]$

Percentage error in cross-sectional area of yarn=1.0 (Ans)