A steel wire of length `4.5m` and cross-sectional area `3xx10^-5m^2` stretches by the same amount as a copper wire of length `3.5m` and cross sectional area of `4xx10^-5m^2` under a given load. The ratio of the Young's modulus of steel to that of copper is

Options

A. `1.3`
B. `1.5`
C. `1.7`
D. `1.9`

Answer

C

Explanation

For copper wire `L_C=3.5m`,
`A_C=4xx10^-5m^2`
For steel wire, `LS=4.5m`,`A_S=3xx10^-5m^2`
As Young's modulus `Y=(((F)/(A)))/(((triangleL)/(L)))`
As applied force F and extension `triangleL` are same for steel and copper wires
`(F)/(triangleL)=(Y_SA_S)/(L_A)=(Y_C)/(L_C)`
where the subscript C and S steel refers to copper and steel respectively.
`(Y_S)/(Y_C)=(L_S)/(L_C)xx(A_C)/(A_S)=((4.5m)xx(4xx10^-5m^2))/((3.5m)xx(3xx10^-5m^2))=1.7`