The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. The cross sectional area of the wire is __________ . (Given, ) [2025]

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Solution

Q.
The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. The cross sectional area of the wire is __________ ${mm}^{2}$ . (Given, $y = 2.0 \times 10^{11} {Nm}^{- 2}$ ) [2023]

Ans.
(40)

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

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

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

   $80 = \frac{1}{2} \times 2 \times 10^{11} \times \frac{{(2 \times 10^{- 2})}^{2}}{40} \times A \times 20$

   $20 = \frac{10^{+ 7}}{20} \times A$

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

   $A = 40 {mm}^{2}$

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