Two wires of the same material have lengths in the ratio `1:2` and their radii are in the ratio `1:sqrt(2)` If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

Options

A. `sqrt(2):2`
B. `2:sqrt(2)`
C. `1:1`
D. `1:2`

Answer

C

Explanation

`Y=(Fl)/(pir^(2)/_\l)` or `/_\l=(Fl)/(pir^(2)Y)`
`/_\lprop1/(r^(2)), /_\l'prop(2l)/((sqrt(2)r)^(2))` or `/_\l'prop 1/(r^(2))`
`:. (/_\l)/(/_\l')=1`