One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end fo another horizontal thin copper wire of lenth 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

Options

A. 0.25
B. 0.5
C. `2.00`
D. `4.00`

Answer

C

Explanation

Force in both the wires will be same.
`DeltaX=(Fl)/(AY)=(Fl)/(pir^(2)Y)`
`rArr(DeltaX_(1))/(DeltaX_(2))=(l_(1))/(r_(1)^(2))xx(r_(2)^(2))/(l_(2))=(l_(1))/(l_(2)).((r_(2))/(r_(1)))^(2)=((2L)/(L))((R)/(2R))^(2)=(1)/(2)`
`(DeltaX_(2))/(DeltaX_(1))=2` (ratio of elongation of the in to thick wire )