Young's modulus of brass and steel are `10 xx 10^(10) N//m^(2)` and `2 xx 10^(11) N//m^(2)`, respectively. A brass wire and a steel wire of the same length are extended by `1 mm` under the same force. The radii of the brass and steel wires are `R_(B)` and `R_(S)` respectively. Then

Options

A. `R_S=sqrt(2)R_B`
B. `R_S=(R_B)/(sqrt2)`
C. `R_S=4R_B`
D. `R_S=(R_B)/(4)`

Answer

B

Explanation

`Y=(F)/(piR^2)xx(l)/(trianglel)`
`F`, `l` and `trianglel` are constant.
`R^2prop(1)/(Y)`
`(R_S^2)/(R_B^2)=(Y_B)/(Y_S)=(10^(11))/(2xx10^(11))=(1)/(2)`
or `(R_S)/(R_B)=(1)/(sqrt2)` or `R_S=(R_S)/(sqrt2)`