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Q.

An iron wire of length 4m and diameter 2mm is loaded with a weight of 8kg. If the Young's modulus 'Y' for iron is 2×10¹¹Nm^–2 then the increase in length of the wire is (g = 10 ms^–2)

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a

1 mm

b

2 mm

c

0.2mm

d

0.5mm

answer is B.

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Detailed Solution

$ℓ = 4 m; r = \frac{2}{2} = 1 \times 10^{- 3} m$
$M = 8 kg; Y = 2 \times 10^{11} N / m^{2}$

$e = \frac{Mgℓ}{{πr}^{2} Y} = \frac{8 \times 10 \times 4}{3.14 \times 10^{- 6} \times 2 \times 10^{11}}$

$\Rightarrow e = \frac{8}{1.57} \times 10^{- 4} m \approx 0.5 mm$

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An iron wire of length 4m and diameter 2mm is loaded with a weight of 8kg. If the Young's modulus 'Y' for iron is 2×1011Nm–2 then the increase in length of the wire is (g = 10 ms–2)