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

Answer

B

Explanation

`Y=(MgL_(1))/(pi r_(1)^(2)l_(1)) and Y=(MgL_(2))/(pi r_(2)^(2)l_(2))`
`(MgL_(1))/(pi r_(1)^(2)l_(1))=(MgL_(2))/(pi r_(2)^(2)l_(2))`
`therefore (l_(1))/(l_(2)) =(L_(1))/(L_(2)) (r_(2)^(2))/(r_(1)^(2)) =(1)/(2) xx ((1)^(2))/((2)^(2)) =(1)/(8)`