MCQ
The elastic potential energy stored in a steel wire of length $20\,m$ stretched through $2 \,m$ is $80\,J$. The cross sectional area of the wire is $.........\,mm ^2$ (Given, $y =2.0 \times 10^{11}\,Nm ^{-2}$ )
  • A
    $38$
  • B
    $36$
  • $40$
  • D
    $34$

Answer

Correct option: C.
$40$
c
Energy per unit volume $=\frac{1}{2} \text { stress } \times \text { strain }$

Energy $=\frac{1}{2} \text { stress } \times \text { strain } \times \text { volume }$

$80=\frac{1}{2} \times Y \times \text { strain }^2 A \times \ell$

$80=\frac{1}{2} \times 2 \times 10^{11} \times \frac{\left(2 \times 10^{-2}\right)^2}{400} \times A \times 20$

$20=\frac{10^{+\prime}}{20} \times A$

$40 \times 10^{-6} m ^2=A$

$A=40\,mm ^2$

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