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Young modulus of a material is defined as
Y=(F/A )(L/l)
Here. F=force applied on material wire
A=cross sectional area of the material wire
L=initial length of the wire
l=increase in length of the wire;
The two rods given in question behave as two wires do.All other things being the same except increase in lengths of rods , thus if these are looking and for the two rods then
l1=(F/A)(L/Y1)
and l2=(F/A)(L/Y2)
For equivalent increase in length of the rod of length L and young modulus is given as
l=l1+l2=FL/(AY1)+FL/(AY2)
Or F (L)/(AY)=FL/A [1/Y1+1/Y2]
Or. 1/Y=(1/Y1+1/Y2)
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