The Young's modulus of brass and steel are respectively `1.0 xx 10^(11) Nm^(-2)` and `2.0 xx 10^(11) Nm^(-2)`. A brass wire and a steel wire of the same length are extended by 1 mm each under the same force. If radii of bras 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

Increase in length,
`Delta L = (FL)/(YA) = (FL)/(Y pi R^(2))`
As F, L and `Delta L` same hence,
`YR^(2)` = constant
`:. 2.0 xx 10^(11) R_(s)^(2) = 1.0 xx 10^(11) R_(s)^(2)`
`implies R_(s) = (R_(B))/(sqrt(2))`