A copper wire and a steel wire of radii in the ratio 1:2, lengths in the ratio 2:1 are stretched by the same force. If the Young's modulus of copper = `1.1 xx 10^11Nm^(-2)` find the ratio of their extensions (young's modulus of steel `= 2 xx 10^11 N//m^2)` .

Explanation

we know `e = (FL)/(pir^2 Y) rArr e_1/e_2 = (L_1/L_2) (r_2/r_1)^2 (Y_2/Y_1) (F/F)`
Here , `r_1: r_2 = 1:2, L_1:L_2 = 2:1`
`Y_1 = 11 xx 10^11 Nm^(-2) , Y_2 = 2.0 xx 10^11 Nm^(-2)`
`e_1/e_2 = 2/1 (2/1)^2 ((2.0 xx 10^11)/(1.1 xx 10^11)) = (16)/(1.1) = 160/11`
`e_1:e_2 = 160:11`