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One end of a horizontal thick copper wir...

One end of a horizontal thick copper wire of length `2L` and radius `2R` is welded to an end of another horizontal thin copper wire of length `L` and radius `R` .When the arrangement is stretched by applying forces at two ends , the ratio of the elongation in the thin wire to that in the thick wire is

A

0.25

B

`0.50`

C

`2.00`

D

`4.00`

Text Solution

Verified by Experts

The correct Answer is:
C

`((F)/(pi(2R)^(2)))/((Deltal_(1))/(2L))= ((F)/(pi(R)^(2)))/((DeltaI_(2)) /(Delta1_(1)))rArr (2FL)/(4piR^(2)Deltal_(1)) = (FL)/(piR^(2)Deltal_(2))`
`rArr 1/(2Deltal_(1)) = 1/(Deltal_(2)) rArr (2FL)/(4piR^(2)Deltal_(1)) =(FL)/(piR^(2)Deltal_(2))`
`rArr " " 1/(2Deltal_(1)) =1/(Deltal_(2)) rArr(Deltal_(2))/(Deltal_(1)) = 2.00`
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