Asteel 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

Asteel wire of length 4.6 m and cross section 3 xx 10^(5)m^(2) stretch

1.	Asteel 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
Answer» Solution :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`