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A wire of length 2m is made from 10 cm^(...

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

A

0.8cm

B

1.6cm

C

2.4cm

D

3.2cm

Text Solution

Verified by Experts

The correct Answer is:
D
`l_(1)= 2m, V_(1) = 10 xx 10^(-6) m^(3), A_(1)= 5 xx 10^(-6) m^(2)`
`Delta l_(1)= 2 xx 10^(-3)m`
`l_(2)= 8m, V_(2)= 10 xx 10^(-6) m^(3), A_(2)= (5)/(4) xx 10^(-6) m^(2)`
`(Delta l_(1))/(Delta l_(2))= (Fl_(1))/(A_(1)Y) xx (A_(2) Y)/(Fl_(2)) = (5)/(4 xx 5) xx (2)/(8)`
`rArr Delta l_(2)= 16 Delta l_(1)= 16 xx 2 xx 10^(-3)`
=3.2cm
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