The Young's modulus of brass and steel are respectively `1.0xx10^(11)N//m^(2)` and `2.0xx10^(11)N//m^(2)` . A brass wire and steel wire of the same length are extended by `1mm` each under the same force. If radii of 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))/(sqrt(2))`
C. `R_(S)=4R_(B)`
D. `R_(S)=(R_(B))/2`

Answer

B

Explanation

Change in length
`DeltaL=(FL)/(YA)=(FL)/(YpiR^(2))`
As `F,L` and `DeltaL` are same hence,
`YR^(2)=a` constant
`:.2.0xx10^(11)R_(S)^(2)=1.0xx10^(11)R_(B)^(2)`
`implies R_(S)=(R_(B))/(sqrt(2))`