Question:
A steel wire length 4.7 m and crossectional area 3.0 x 10^-5 m^2 streches by the same amount as copper wire of length 3.5 m and crossectional area 4.0 x 10^-5 m^2 under a given load. Whta is the ratio of the Young
Answer:
Length of the steel wire L1 = 4.7 m
Area of cross section of the steel wire A1 = 3.0 x 10-5 m2
Length of the copper wire L2 = 3.5 m
Area of cross section of the steel wire A1 = 4.0 x 10-5 m2
Change in length = ΔL
Force = F
Young s modulus of the steel wire Y1 = F1 x L1/A1 x ΔL = F x 4.7/ 3.0 x 10-5 x ΔL.....(1)
Young s modulus of the Copper wire Y2 = F2 x L2/A2 x ΔL = F x 3.5/ 4.0 x 10-5 x ΔL.....(2)
Y1/Y2 = F x 4.7/ 4.0 x 10-5 x ΔL/ F x 3.5/ 4.0 x 10-5 x ΔL
= 4.7 x 4.0 x 10-5 / 3.5 x 4.0 x 10-5
=1.8 :1
The ration of Young s modulus of the Copper wire 1.8 :1 .
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