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

Options

A. `R_(s)=sqrt(2)R_(B)`
B. `R_(S)=(R_(B))/(sqrt(2))`
C. `R_(S)=4R_(B)`
D. `R_(S)=(R_(B))//4`

Answer

B

Explanation

`Y=(F//A)/((/_\l)//l)=(Fl)/(/_\lA)=(Fl)/(/_\l(piR^(2)))`
Hence `Yprop1/(R^(2))`
`(Y_(B))/(Y_(S))=(R_(S)^(2))/(R_(B)^(2))`
`(10xx10^(10))/(20xx10^(10))=(R_(2)^(2))/(R_(B)^(2)`
`R_(B)^(2)=2R_(S)^(2)`
`R_(B)=sqrt(2)Rs`
`impliesR_(S)=(R_(B))/(sqrt(2)`