A steel wire of length 4.87 mm and cross-section `3.0 xx 10^(-5) m^(2)` stretches by the same amout as a copper wire of length 3.5 m and cross -section `4.0 xx 10^(-5) m^(2)` under a given load . White is the ratio of the Young's modulus of steel so that of copper ?

Options

A. 1.5 : 2
B. 1.8 : 2
C. 1.5 : 1
D. 1.8 : 1

Answer

D

Explanation

(d) As given for steel wire
`A_(1)=3xx10^(-5)m^(2), l_(1)=4.7 m, Deltal_(1)=Deltal, F_(1)=F`
For copper wire,
`A_(2)=4xx10^(-5)m^(2)`
`l_(2)=3.5m, Deltal_(2)=Deltal,F_(2)=F`
Let `Y_(1)` and `Y_(2)` be the Young's modulus of steel wire and copper wire , respectively.
So, `Y_(1)=(F_(1))/(A_(1))xx(l_(1))/(Deltal_(1))=(F)/(3xx10^(-5))xx(4.7)/(Deltal)`
and `Y_(2)=(F_(2)xxl_(2))/(A_(2)xxDeltal_(2))=(Fxx3.5)/(4xx10^(-5)xxDeltal)`
`(Y_(1))/(Y_(2))=(4.7xx4xx10^(-5))/(3.5xx3.0xx10^(-5))=1.8`
So, `Y_(1):Y_(2)=1.8:1`