The work done in deforming body is given by-Turito

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General

Easy

Physics-

The work done in deforming body is given by

Physics-General

$s t r e s s \times s t r a i n$
$\frac{1}{2} (s t r e s s \times s t r a i n)$
$s t r e s s / s r a i n$
Strain/stress

Answer:The correct answer is: $fraction numerator 1 over denominator 2 end fraction left parenthesis s t r e s s cross times s t r a i n right parenthesis$ Let 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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