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Question

A composite bar of length L equals L subscript 1 end subscript plus L subscript 2 end subscript is made up from a rod of material 1 and of length L1 attached to a rod of material 2 and of length L2 as shown. If alpha subscript 1 end subscript and alpha subscript 2 end subscript are their respective coefficients of linear expansion, then equivalent coefficient of linear expansion for the composite rod is:

  1. fraction numerator alpha subscript 1 end subscript L subscript 2 end subscript plus alpha subscript 2 end subscript L subscript 1 end subscript over denominator L end fraction    
  2. fraction numerator alpha subscript 1 end subscript L subscript 2 end subscript plus alpha subscript 2 end subscript L subscript 2 end subscript over denominator L end fraction    
  3. fraction numerator alpha subscript 1 end subscript L subscript 1 end subscript plus alpha subscript 2 end subscript L subscript 2 end subscript over denominator L end fraction    
  4. fraction numerator alpha subscript 1 end subscript alpha subscript 2 end subscript open parentheses L subscript 1 end subscript superscript 2 end superscript plus L subscript 2 end subscript close parentheses over denominator open parentheses alpha subscript 1 end subscript L subscript 1 end subscript plus alpha subscript 2 end subscript L subscript 2 end subscript close parentheses end fraction    

The correct answer is: fraction numerator alpha subscript 1 end subscript L subscript 1 end subscript plus alpha subscript 2 end subscript L subscript 2 end subscript over denominator L end fraction


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