Two wires A and B are of the same material. Their lengths are in the ratio 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, then increase in length will be in the ratio

Options

A. `1:2`
B. `4:1`
C. `1:8`
D. `1:4`

Answer

C

Explanation

If a wire of length L and radius r is stretched by `Delta L` by applying a force F, then
`Delta L = (FL)/(pi r^(2) Y)`
`:. Delta L_(A) = (FL_(A))/(pi r_(A)^(2)Y) and Delta L_(B) = (FL_(B))/(pi r_(B)^(2) Y) or (Delta L_(A))/(Delta L_(B)) = (L_(A))/(L_(B)) ((r_(B))/(r_(A)))^(2)`
Given `(L_(A))/(L_(B)) = (1)/(2) and (r_(A))/(r_(B)) (2)/(1) :. (Delta L_(A))/(Delta L_(B)) = (1)/(2) xx (1)/((2)^(2)) = (1)/(8)`