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A brass wire of radius 1 mm and of length 1m is stretched by applying a force of 10N. If the increase in length is 0.5mm, Then the Young's modulus of the wire is

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$8.3 \times 10^{9} N / m^{2}$

$5.2 \times 10^{9} N / m^{2}$

$6.4 \times 10^{9} N / m^{2}$

$4.3 \times 10^{9} N / m^{2}$

answer is B.

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Detailed Solution

$y = \frac{F L}{A e}$

$= \frac{10 \times 1}{π \times 10^{- 6} \times \frac{1}{2} \times 10^{- 3}} = \frac{2 \times 10^{4}}{3.14 \times 10^{- 6}}$

$= 0.636 \times 10^{10}$

$= 6.4 \times 10^{9} N / m^{2}$

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