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Two wires of copper having the length in...

Two wires of copper having the length in the ratio `4 : 1` and their radii ratio as `1 : 4` are stretched by the same force. The ratio of longitudinal strain in the two will be

A

`1:16`

B

`16:1`

C

`1:64`

D

`64:1`

Text Solution

Verified by Experts

The correct Answer is:
D
`(l_(1))/(l_(2))= 4, (r_(1))/(r_(2))= (1)/(4)`
`Delta l= (Fl)/(AY)`
`rArr Delta l prop (l)/(A) rArr Dleta l prop (l)/(r^(2))`
`rArr (Delta l_(1))/(Delta l_(2)) = ((l_(1))/(l_(2))) ((r_(2))/(r_(1)))^(2) = (4) (4)^(2)`
`rArr (Delta l_(1))/(Delta l_(2))= 64:1`
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