Two wires are made of same metal. The length of the first wire is half that of the second wire and its diameter is double that of the second wire. If equal loads are applied on both wires, find the ratio of increases in their lengths.

Explanation

`Y=(F//A)/(Deltal//l)impliesDletal=(Fl)/(Ay)=(Fl)/(pir^(2)Y)`
`(Deltal_(1))/(Delta_(1))/(Deltal_(2))=(Deltal_(1))/(Deltal_(2))=(4Fl_(1))/(pid_(1)^(2)Y)xx(pid_(2)^(2)Y)/(4Fl_(2))`
`=(l_(1))/(l_(2))xx(d_(2)^(2))/(d_(1)^(2))=1/2xx1/((2)^(2))=1/8`