GATE (TF) Textile 2013 Question Paper Solution | GATE/2013/TF/27

Question 27 (Textile Engineering & Fibre Science)

The relationship between load (y) is N and elongation (x) in mm of a cotton fabric is y=\sqrt{x}. If the breaking elongation of the fabric is 9 mm, the work of rupture, in N.mm is ____.

Answer / Solution
Given–

y=\sqrt x
Where, y is load and x is elongation

Breaking elongation(e)=9 mm

Work of rupture(N.mm)=?

Calculation–

Work of rupture is the area under the load elongation curve.
i.e.,
Work of rupture=\int_{0}^{e} y dx

Work of rupture=\int_{0}^{9} \sqrt x dx

Work of rupture=\int_{0}^{9} x^\frac{1}{2} dx

Work of rupture= [\frac{x^\frac{3}{2} }{\frac{3}{2}}]_{0}^{9}

Work of rupture= \frac{2}{3}\times [ x^\frac{3}{2}]_{0}^{9}

Work of rupture= \frac{2}{3} \times[9^\frac{3}{2}-0^\frac{3}{2}]

Work of rupture= \frac{2}{3} \times[3^(2 \times\frac{3}{2})-0^\frac{3}{2}]

Work of rupture= \frac{2}{3} \times[3^3-0]

Work of rupture= \frac{2}{3} \times[27-0]

Work of rupture= \frac{2}{3} \times 27

Work of rupture= 2 x 27/3

Work of rupture= 2 x 9

Work of rupture=18 N.mm (Answer)
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