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A steel wire of length 10 m, radius 0.1 cm, and density 7860 kg/m³ has a Young’s modulus of 200 GPa. It hangs from the ceiling with a load 25 kg attached at the other end. The elongation produced in the wire is

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1 mm

4 mm

2 mm

0.5 mm

answer is B.

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Detailed Solution

$e = \frac{Fl}{AY} = \frac{mgl}{{πr}^{2} Y} = \frac{25 x 10 x 10}{3.14 x 10^{- 6} x 200 x 10^{9}}$
$= \frac{25}{6.28} x 10^{- 3} m$ = 3.9 mm $≃$ 4 mm

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