Two rods of identical dimension with youngs modulli Y1 and Y2 are joined end to end . The equivalent youngs modulus for the composite rod is (if the equivalent rod is also having same dimension as of the original rods)

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Solution

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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