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 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 )