A steel wire of length `4*0m` and cross-section `25 mm^(2)` strectched by the same anount as a copper wire of length `3*0 m` and cross-section `32 mm^(-2)` under a given load. Find the ration of the young's modulus of steel to that of copper?

Explanation

Here, steel wire, `l_(1)=4.0 m`, area of cross - section , `A_(1)=25 mm^(2) = 25 xx 10^(-6) m^(2)`
For copper wire, `l_(2)=3.0m, A_(2)=32xx 10^(-6)m^(2)`
Let `Y_(1)Y_(2)` be the young's modulus of steel and copper respectively. Let F be the load applied to each wire. Let `Delta l_(1)` and `Delta l_(2)` be the extension in the steel wire and copper wire respectively.
Then `Y_(1)=(Fl_(1))/(A_(1)Delta l_(1)) = (Fxx 4.0)/((25 xx 10^(-6)Delta l_(1))`
`Y_(2) =(Fl_(2))/(A_(2)Delta l_(2)) = (Fxx 3.0)/((32 xx 10^(-6)Delta l_(2))`
`(Y_1)/(Y_2) = (Fl_(1))/(A_(1)Delta l_(1)) = (Fxx 4.0)/((25 xx 10^(-6)Delta l_(1))) xx (Fxx 3.0)/((32 xx 10^(-6)Delta l_(2))) = (4 xx 32)/(25 xx 3)` ( `:. Delta l_(1) -Delta l_(2))`
`=1.71`.