Consider two aluminum rods of length 1 m, one twice as thick as the other. If a compressive force F is applied to both rods, their lengths are reduced by LaTeX: \Delta L_{thick}ΔLthickand LaTeX: \Delta L_{thin}ΔLthin, respectively.

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Consider two aluminum rods of length 1 m, one twice as thick as the other. If a compressive force F is applied to both rods, their lengths are reduced by  and , respectively.The ratio ΔLthick rod/ΔLthin rod is:

a.) =1

b.) <1

c.) >1

The ratio is less than 1 i.e   option B is correct

Explanation:

The Young Modulus of a material is generally calculated with this formula

 Where is the stress =

              is the strain =

  Making Strain the subject

now in this question we are that the same tension was applied to both wires so

      would be constant

Hence

for the two wire we have that

      Looking at young modulus formula

Now we are told that a comprehensive force is applied to the wire so for this question

                is constant

And given that the length are the same

so  

Now we are told that one is that one rod is twice as thick as the other

So it implies that one would have an area that would be two times of the other

  Assuming that

So

From the question the length are equal

So  

Hence the ratio is less than 1