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Q.

A wire whose cross - sectional area is 4 mm $^{2}$ is stretched by 0.1 mm by a certain load. If a similar wire of double the area of cross - section is under the same load, then the elongation would be

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a

0.005mm

b

0.05mm

c

5mm

d

0.5mm

answer is B.

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Detailed Solution

$\large A_1=4mm^2=4\times10^{-6}m^2$
$\large {e_1} = 0.1mm = 0.1 \times {10^{ - 3}}m = 1 \times {10^{ - 4}}m$
$\large {A_2} = 2{A_1},e\alpha \frac{1}{A}$
$\large {e_2} = \frac{{{A_1}}}{{{A_2}}} \times {e_1} = \frac{{{A_1}}}{{2{A_1}}} \times 0.1 = 0.05mm$

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A wire whose cross - sectional area is 4 mm 2 is stretched by 0.1 mm by a certain load. If a similar wire of double the area of cross - section is under the same load, then the elongation would be