Question

two wires of equal cross section but one made of steel and the other of copper are joined end to end .when the combination is kept under tension,the elongation the two wires are found to be equal .given youngs moduli of steel and copper are 2 *10^11 NM ^-2 AND 1.1 *10^11 NM^-2 .FIND RATIO BETWWEN THE LENGTH OF STEEL AND COPPER WIRE?

Answer 1

Since two wires(different materials) of same c/s is joined end to end and subjected to a same tension load, hence stress induced in both the rods will be same. Stress = load/area.
Now strain = dL/L
Youngs modulus = Stress /Strain
dL is also mentioned as equal for both the rods.

So, equate both the stresses :
(Youngs modulus x strain) is equal for both.

2x10^11 x dL/Lsteel = 1.1x10^11 x dL/Lc

2/Ls = 1.1/Lc
Ls/Lc = 2/1.1 =

Answer 2

Y = σ / ε = F * L / A ΔL

      L = length of the rod
      F = tension = equal in both rods as they are joined end to end
      ΔL = elongation = same in both rods
      A = area of cross section = same in both

Hence  Y / L = constant
 
   Y1 / Y2 = L1 / L2
   L1 /L2 = Y1 / Y2
              = 2 * 10¹¹ / 1.1 * 10¹¹
              = 1.81      Length of steel to copper wire.