Q. 4

# A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end and the combination is subjected to a tension. Find the ratio of (a) the stresses developed in the two wires and (b) the strains developed. Y of steel = 2 × 10^{11} N m^{-2}. Y of copper = 1.3 × 10 11 N m^{-2}.

Answer :

(a) 1

(b)

Here, the wires are of equal length(L) and cross-sectional area(A). Let the force produced by the load across them be F which is same for both the wires.

Young modulus of the steel,

Young modulus of the copper,

(a) Let the stress in steel wire be and that in copper be

Now, and

Hence,

(b) The strain is given by

The strain in the steel wire is

The strain in the copper wire is

hence,

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