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?
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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
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