A copper rod with length 1.4 m and area of cross-section of `2 cm^2` is fastened to a steel rod with length L and cross-sectional area `1 cm^2`. The compound rod is subjected to equal and opposite pulls to magnitude `6.00xx10^4` N at its ends .
(a) Find the length L of the steel rod if the elongation of the two rods are equal .
(b) What is stress in each rod ?
(c ) What is the strain in each rod ? `[Y_"steel"=2xx10^11 Pa , Y_(Cu)=1.1xx10^11 Pa]`

Explanation

`Deltal_(CU)=Deltal_(steel)`
`(Fl_C)/(A_CY_C)=(Fl_S)/(A_S Y_S)rArr l_S=(A_S/A_C)(Y_S/Y_C)l_C`
or `L=(1.0/2.0)((2xx10^11)/(1.1xx10^11))1.40` =1.27 m
(b) `sigma_C=F/A_C=(6xx10^4)/(2xx10^(-4))=3xx10^8 N//m^2`
and `sigma_S=F/A_S=(6xx10^(4))/(1xx10^(-4))=6xx10^6 N//m^2`
(c ) `epsilon_c=sigma_c/Y_c=2.7xx10^(-3)`
`epsilon_s=sigma_S/Y_s=3.0xx10^(-3)`