Question

Q1. A steel wire of length 4.7 m and cross-sectional area 3.0 × 10-5 m2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10–5 m2 under a given load. What is the ratio of the Young’s modulus of steel to that of copper? ​

Answer 1

Answer:

Length of the Steel wire :

= L^1

4.7 m <br> Area of cross- sectionof the steel wire,

= A^ 1= 3.0 ×10^ -5 m^2

< br > length of the copper wire :

= L^2

= 3.5 m<br> Area cross section of the copper wire

=A^2 = 4.0× 10^-5 m^2

<br> change in length

= ∆L^1 = ∆L^2 = ∆L

< br > Force applied in both the casses = F <br> Young's modulus of the steel wire <br>

= Y ^1 = F^1 / A^1 = L^1 / ∆L

< br >

F × 3.5 / 4.0 ×10^5 × ∆L .... ( ii )

<br > Dividing (1) by (2) , we get < br >

Y^1 / Y^2 = 4.7 × 4.0×10^5/

3.0 × 10^ -5 × 3.5 =1.79 :1

< br > The ratio of young modulus of steel of that of copper is 1.79:1