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Q.

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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a

4 mm

b

0.5 mm

c

1 mm

d

2 mm

answer is B.

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Detailed Solution

Mass of the wire is very small compared to the suspended load of 25 kg. we can ignore it.
\large e = \frac{{Fl}}{{AY}} = \frac{{mgl}}{{\pi {r^2}Y}} = \frac{{25 \times 10 \times 10}}{{3.14 \times {{10}^{ - 6}} \times 200 \times {{10}^9}}}
\large = \frac{{25}}{{6.28}} \times {10^{ - 3}}\;m = 3.9\;mm \simeq 4\;mm

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