A steel wire of length 4.6 m and cross section `3 xx 10^(5)m^(2)` stretches by the same amount as a copper wire of length 4.0 m and cross section `4.0 xx 10^(-5) m^(2)` under the same load. Find the ratio of the Young.s modulus of steel to that of copper

Explanation

Elongation `=(Mgl)/(pir^(2)Y)=(Mgl)/(AY)`
Since the elongations are the same in both cases under the same load `(l_(s))/(A_(s)Y_(s))=(l_(C_(u)))/(A_(C_(u))Y_(C_(u)))`
`:.(Y_(s))/(Y_(C_(u)))((l_(s))/(l_(C_(u))))((A_(C_(u)))/(A_(S)))=(4.6)/(4.0)((4xx10^(-5))/(3xx10^(-5)))=(4.6)/(3)=(23)/(15)`
So the ratio of their moduli of clasticity is `23:15`