Two pieces of wire, A and B of the same material have their lengths in the ratio `1:3` and their diameters are in the ratio `2:1` . If they are stretched by the same force, their elongations will be in the ratio

Options

A. `2:1`
B. `1:6`
C. `1:12`
D. `8:1`

Answer

C

Explanation

For constant force and same material
`=(l_(1))/(l_(2)) = (L_(1))/(L_(2))xx(r_(2)^(2))/(r_(1)^(2))=(1)/(12)`