A steel wire of length 4.7 m and cross-sectional area `3.0 xx 10^-5 m^2` stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of `4.0 xx 10^-5 M^2` under a given load. What is the ratio of the Young’s modulus of steel to that of copper?

Explanation

We are given:
For steel, length of wire
`l_S = 4.7 m`
Area of cross-section `a_S = 3xx10^(-5) m^2 implies` For copper, length of wire, `l_C = 3.5 m`
Area of cross section `a_C = 4xx10^(-5) m^2`
If F be the stretching force, I be the increase in length in each case and `Y_S` and `Y_C` be the Young.s moduli of steel and copper respectively,
We are to calculate: Ratio of Young.s modulus of steel to that of copper.
Using relation:
`Y=(Fl)/(a Delta l)` For steel `Y_S=(F l_S)/(a_S l)` and For copper `Y_C=(F l_C)/(a_C l)`
Therefore, `(Y_S)/(Y_C)=((F l_S)/(a_S l))/((F l_C)/(a_C l))=(l_S a_C)/(l_C a_S)=(4.7xx4xx10^(-5))/(3.5xx3xx10^(-5))= 1.8`