A wire of length `2m` is made from `10 cm^(2)` of copper. A force F is applied so that its length increases by `2mm`. Another wire of length `8m` is made from the same volume of copper. If the force F is applied to it, its length will increase by

Options

A. 0.8 cm
B. 1.6cm
C. 2.4 cm
D. 3.2 cm

Answer

D

Explanation

As `I+(FL)/(AY) = (FL^(2))/((AL)Y) =(FL^(2))/(VY)`
`therefore I prop L^(2)` , if volume of the wire remains constant .
`(l_(2))/(l_(1))=((L_(2))/(L_(1)))^(2) = ((8)/(2))^(2) = 16`
`therefore l_(2) = 16 xx l_(1) = 16 xx 2 = 32 mm` ltbrlt ` = 3.2 cm`