When a certain weight is suspended from a long uniform wire, its length increases by `1 cm`. If the same weight is suspended from another we of the same material and length but having a diameter half of the first one, the increases in length will be

Options

A. `0.5cm`
B. `2cm`
C. `4cm`
D. `8cm`

Answer

C

Explanation

`Y=(Fl)/(a/_\l)` or `/_\lprop1/a, /_\l prop 1/(D^(2))`
`(/_\l_2)/(/_\l_1)=(D_(1)^(2))/(D_(2)^(2)) =4` or `/_\l_(2)=4/_\l_(1)=4cm`