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The work done in deforming body is given by

Physics-General

  1. s t r e s s blank cross times s t r a i n    
  2. fraction numerator 1 over denominator 2 end fraction left parenthesis s t r e s s cross times s t r a i n right parenthesis    
  3. s t r e s s divided by s r a i n    
  4. Strain/stress    

    Answer:The correct answer is: fraction numerator 1 over denominator 2 end fraction left parenthesis s t r e s s cross times s t r a i n right parenthesisLet L be length of body, A the area of cross-section and l the increase in length.
    S t r e s s equals fraction numerator F over denominator A to the power of ´ end exponent end fraction s t r a i n equals fraction numerator l over denominator L end fraction
    Force necessary to deform the body is
    F equals fraction numerator Y A over denominator L end fraction l
    If body is deformed by a distance, then
    W o r k blank d o n e equals F cross times d l equals fraction numerator Y A over denominator L end fraction l d l
    W equals not stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator Y A over denominator L end fraction l d l equals fraction numerator Y A over denominator L end fraction open square brackets fraction numerator l to the power of 2 end exponent over denominator 2 end fraction close square brackets subscript 0 end subscript superscript l end superscript equals fraction numerator 1 over denominator 2 end fraction Y A fraction numerator l to the power of 2 end exponent over denominator L end fraction
    equals fraction numerator 1 over denominator 2 end fraction open parentheses Y fraction numerator l over denominator L end fraction close parentheses open parentheses fraction numerator l over denominator L end fraction close parentheses open parentheses A L close parentheses
    equals fraction numerator 1 over denominator 2 end fraction open parentheses s t r e s s cross times s t r a i n close parentheses cross times v o l u m e
    Hence, work done for unit volume is
    W equals fraction numerator 1 over denominator 2 end fraction s t r e s s cross times s r a i n.

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