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. `1.8 : 1`
B. `2.8 : 1`
C. `3.8 : 1`
D. `4.8 : 1`

Answer

A

Explanation

Given, for steel wire,
`A_(1) = 3.0 xx 10^(-5) m^(2), L_(1) = 4.7 m, Delta L_(1) = Delta L, F_(1)= F`
For copper wire, `A_(2) = 4.0 xx 10^(-5) m^(2), L_(2) = 3.5 m, Delta_(2) = Delta L, F_(2) = F`
Let `Y_(1) Y_(2)` be the young.s modulus of steel wire and copper wire respectively.
`:. Y_(1) = (F_(1) L_(1))/(A_(1) Delta L_(1)) = (F xx 4.7)/(3.0 xx 10^(-5) xx Delta L)`
and `Y_(2) = (F_(2) L_(2))/(A_(2) Delta L_(2)) = (F xx 3.5)/(4 xx 10^(-5) xx Delta L)`
`:. (Y_(1))/(Y_(2))= (4.7 xx 4 xx 10^(-5))/(3.0 xx 10^(-5) xx 3.5) = 1.8`
Hence `Y_(1) : Y_(2) = 1.8 : 1`