A steel wire of 1 m long and 1 mm^2 cross section area is hanging from rigid end. When weight of 1 kg is hung from it then change in length will be

Q: A steel wire of 1 m long and 1 mm2 cross section area is hanging from rigid end. When weight of 1 kg is hung from it then change in length will be (given Y = 2 × 1011 N/m2)

(a) 0.5 mm

(b) 0.25 mm

(c) 0.05 mm

(d) 5 mm

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Ans: (c)
Sol: $\displaystyle \Delta L = \frac{F L}{A Y}$

$\displaystyle \Delta L = \frac{1 \times 10 \times 1}{1 \times 10^{-6} \times 2 \times 10^{11}}$

$\displaystyle \Delta L = 0.5 \times 10^{-4}$

0.05 mm